function evaluation

Practise function evaluation with an original VectorPaths question, worked explanation and related VCE Methods practice.

1 practice marks

Original practice question

Let $f(x) = 2x + 3$ and let $f^{-1}$ be the inverse function of $f$. Find the value of $f(f^{-1}(5)) + f^{-1}(f(7))$.

Worked explanation

• Use inverse function property

  \[f(f^{-1}(5)) = 5 \quad \text{and} \quad f^{-1}(f(7)) = 7\]

• Sum the results

  \[f(f^{-1}(5)) + f^{-1}(f(7)) = 5 + 7 = 12\]

$12$

Original VectorPaths practice; not an official VCAA question or marking rubric.