Question Type 8: Solving questions with the values of inverses Exercises

Given an invertible function $f$ with $f(2)=5$, $f(3)=6$, $f(6)=8$ and $f\left(\frac{1}{6}\right)=18$, find $f^{-1}(18)$.

Suppose $f$ is invertible and $f(2)=5$, $f(3)=6$, $f(6)=8$, $f(\frac{1}{6})=18$. Find $f^{-1}(8)$.

Let $k(x)=f^{-1}\bigl(f(x)-12\bigr)$ for an invertible function $f$ with $f(2)=5$, $f(3)=6$, $f(6)=8$, and $f\left(\frac{1}{6}\right)=18$.

Find $k\left(\frac{1}{6}\right)$.

Define $g(x)=f^{-1}(x)+2$ for an invertible $f$ with $f(2)=5$, $f(3)=6$, $f(6)=8$, $f(\tfrac{1}{6})=18$. Find $g(6)$.

Let $f$ be an invertible function with $f(2)=5$, $f(3)=6$, $f(6)=8$ and $f(\frac{1}{6})=18$. Determine $f^{-1}(5)$.

The function $f$ is invertible. Given that $f(2)=5$, $f(3)=6$, $f(6)=8$, and $f\left(\frac{1}{6}\right)=18$, find the value of $f^{-1}\left(f\left(\frac{1}{6}\right)\right)$.

Evaluate $f^{-1}\bigl(f\bigl(f^{-1}(8)\bigr)\bigr)$.

Let $f$ be invertible with $f(2)=5$, $f(3)=6$, $f(6)=8$, $f(\frac{1}{6})=18$. If $f^{-1}(x)=3$, find $x$.

Find the value of $p(6)$.

Let $f$ be an invertible function such that $f(2)=5$, $f(3)=6$, $f(6)=8$ and $f(\tfrac{1}{6})=18$. Find $f^{-1}(6)$.

Let $f$ be invertible with $f(2)=5$, $f(3)=6$, $f(6)=8$, $f\left(\frac{1}{6}\right)=18$. Evaluate $f\bigl(f^{-1}(6)\bigr)$.

Let $h(x)=f\bigl(f^{-1}(x)-1\bigr)$, where $f$ is invertible and $f(2)=5$, $f(3)=6$, $f(6)=8$, $f(\frac{1}{6})=18$. Determine $h(6)$.