0606 · Notes & worked examples
Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.
Recall
Maths4U Original · Short practice
Let \(f{\left(x \right)} = 4 x + 21\), \(g{\left(x \right)} = \left(x - 1\right)^{2}\), \(\displaystyle h=1\) and \(\displaystyle u=5\). Write fg=f∘g. Restrict g to \(\displaystyle x\ge h\) when solving equations.
Find f(g(u)).
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Fresh review variant
Maths4U Original · Short practice
Let \(f{\left(x \right)} = 2 x + 22\), \(g{\left(x \right)} = \left(x - 2\right)^{2}\), \(\displaystyle h=2\) and \(\displaystyle u=4\). Write fg=f∘g. Restrict g to \(\displaystyle x\ge h\) when solving equations.
Find f(g(u)).
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Method
Maths4U Original · Short practice
Let \(f{\left(x \right)} = 2 x + 22\), \(g{\left(x \right)} = \left(x - 2\right)^{2}\), \(\displaystyle h=2\) and \(\displaystyle u=4\). Write fg=f∘g. Restrict g to \(\displaystyle x\ge h\) when solving equations.
Find g(f(u)).
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Fresh review variant
Maths4U Original · Short practice
Let \(f{\left(x \right)} = 3 x + 23\), \(g{\left(x \right)} = \left(x - 3\right)^{2}\), \(\displaystyle h=3\) and \(\displaystyle u=6\). Write fg=f∘g. Restrict g to \(\displaystyle x\ge h\) when solving equations.
Find g(f(u)).
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Apply
Maths4U Original · Short practice
Let \(f{\left(x \right)} = 3 x + 23\), \(g{\left(x \right)} = \left(x - 3\right)^{2}\), \(\displaystyle h=3\) and \(\displaystyle u=6\). Write fg=f∘g. Restrict g to \(\displaystyle x\ge h\) when solving equations.
Find f(g(u))−g(f(u)).
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Fresh review variant
Maths4U Original · Short practice
Let \(f{\left(x \right)} = 4 x + 24\), \(g{\left(x \right)} = \left(x - 4\right)^{2}\), \(\displaystyle h=4\) and \(\displaystyle u=8\). Write fg=f∘g. Restrict g to \(\displaystyle x\ge h\) when solving equations.
Find f(g(u))−g(f(u)).
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Check understanding
Maths4U Original · Short practice
Let \(f{\left(x \right)} = 4 x + 24\), \(g{\left(x \right)} = \left(x - 4\right)^{2}\), \(\displaystyle h=4\) and \(\displaystyle u=8\). Write fg=f∘g. Restrict g to \(\displaystyle x\ge h\) when solving equations.
On \(\displaystyle x\ge h\), solve \(\displaystyle f(g(x))=f(g(u))\) for x.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Fresh review variant
Maths4U Original · Short practice
Let \(f{\left(x \right)} = 2 x + 25\), \(g{\left(x \right)} = \left(x - 1\right)^{2}\), \(\displaystyle h=1\) and \(\displaystyle u=3\). Write fg=f∘g. Restrict g to \(\displaystyle x\ge h\) when solving equations.
On \(\displaystyle x\ge h\), solve \(\displaystyle f(g(x))=f(g(u))\) for x.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.