Maths4U Original · Short practice

\(f(x)=2 x + 7\) with domain \(\left[0, 3\right]\).

Find f at its lower domain endpoint.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=3 x + 8\) with domain \(\left[1, 5\right]\).

Find f at its lower domain endpoint.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=3 x + 8\) with domain \(\left[1, 5\right]\).

Find f at its upper domain endpoint.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=4 x + 9\) with domain \(\left[2, 7\right]\).

Find f at its upper domain endpoint.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=4 x + 9\) with domain \(\left[2, 7\right]\).

Find \(f^{-1}(21)\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=5 x + 10\) with domain \(\left[-2, 4\right]\).

Find \(f^{-1}(5)\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=5 x + 10\) with domain \(\left[-2, 4\right]\).

Find the gradient of the inverse rule.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=2 x + 3\) with domain \(\left[-1, 2\right]\).

Find the gradient of the inverse rule.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=3 x + 10\), \(g(x)=\left(x - 3\right)^{2}\) and \(\displaystyle t=6\). Both rules have domain ℝ. Use fg=f∘g and gf=g∘f.

Find f(g(t)).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=4 x + 2\), \(g(x)=\left(x + 2\right)^{2}\) and \(\displaystyle t=2\). Both rules have domain ℝ. Use fg=f∘g and gf=g∘f.

Find f(g(t)).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=4 x + 2\), \(g(x)=\left(x + 2\right)^{2}\) and \(\displaystyle t=2\). Both rules have domain ℝ. Use fg=f∘g and gf=g∘f.

Find g(f(t)).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=5 x + 3\), \(g(x)=\left(x + 1\right)^{2}\) and \(\displaystyle t=4\). Both rules have domain ℝ. Use fg=f∘g and gf=g∘f.

Find g(f(t)).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=5 x + 3\), \(g(x)=\left(x + 1\right)^{2}\) and \(\displaystyle t=4\). Both rules have domain ℝ. Use fg=f∘g and gf=g∘f.

Find g(f(t))−f(g(t)).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=2 x + 4\), \(g(x)=x^{2}\) and \(\displaystyle t=2\). Both rules have domain ℝ. Use fg=f∘g and gf=g∘f.

Find g(f(t))−f(g(t)).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=2 x + 4\), \(g(x)=x^{2}\) and \(\displaystyle t=2\). Both rules have domain ℝ. Use fg=f∘g and gf=g∘f.

Find the coefficient of \(\displaystyle x^{2}\) in f(g(x)).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=3 x + 5\), \(g(x)=\left(x - 1\right)^{2}\) and \(\displaystyle t=4\). Both rules have domain ℝ. Use fg=f∘g and gf=g∘f.

Find the coefficient of \(\displaystyle x^{2}\) in f(g(x)).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle f(x)=\frac{7}{x + 8}\) on its full real domain.

Find the excluded input of f.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle f(x)=\frac{8}{x + 9}\) on its full real domain.

Find the excluded input of f.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle f(x)=\frac{8}{x + 9}\) on its full real domain.

Find \(\displaystyle f^{-1}(\frac{8}{11})\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle f(x)=\frac{2}{x + 2}\) on its full real domain.

Find \(\displaystyle f^{-1}(\frac{2}{5})\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle f(x)=\frac{2}{x + 2}\) on its full real domain.

Find \(f^{-1}(1)\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle f(x)=\frac{2}{x + 9}\) on its full real domain.

Find \(f^{-1}(1)\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle f(x)=\frac{3}{x + 3}\) on its full real domain.

Find \(f^{-1}(2)\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle f(x)=\frac{4}{x + 4}\) on its full real domain.

Find \(f^{-1}(2)\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.