Composite functions and their domains: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Let \(f(x)=2x+1\), \(g(x)=x^2\). Find \(f(g(3))\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Composite functions and their domains: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
With \(f(x)=2x+1\), \(g(x)=x^2\), find \(g(f(3))\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Composite functions and their domains: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Let \(f(x)=\sqrt{x}\), \(g(x)=x-4\). What is the real domain of \(f(g(x))\)?Choose one answer.
Composite functions and their domains: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Let \(f:A\to B\) and \(g\) have domain \(C\). When can \(g\circ f\) use every input of \(f\)?Choose one answer.
Composite functions and their domains: check 5
Difficulty: ★★☆Info
Maths4U Original · Short practice
Let \(\displaystyle f(x)= \frac{1}{x}\), \(x\ge2\). What is its range?Choose one answer.
Composite functions and their domains: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
For \(f(x)=3x-2\), \(g(x)=x^2\), find \(f(g(2))\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Composite functions and their domains: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
For \(f(x)=3x-2\), \(g(x)=x^2\), find \(g(f(2))\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Composite functions and their domains: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
For \(f(x)=\sqrt{x}\), \(g(x)=x-7\), enter the lower endpoint of the real domain of \(f(g(x))\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Composite functions and their domains: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Let \(f(x)=2x\) on \([0,a]\), \(a>0\), and let g have domain \([0,10]\). Find the greatest a for which \(g\circ f\) is defined for every input of f.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Composite functions and their domains: review variant 5
Difficulty: ★★☆Info
Maths4U Original · Short practice
For \(\displaystyle f(x)= \frac{3}{x}\), \(x\ge2\), enter the upper endpoint of its range.Enter one number or fraction. Round decimals to at least six decimal places when needed.