Question

use the table to answer the question.

the table shows the function values of the one-to-one function $f(x)$. evaluate $f(3)-f^{-1}(5)-2f^{-1}(3)$.

$f(3) - f^{-1}(5) - 2f^{-1}(3) = \square$
(5 points)

Explanation:

Step1: Find $f(3)$ from table

From the table, when $x=3$, $f(3)=9$

Step2: Find $f^{-1}(5)$

For inverse function, $f^{-1}(y)=x$ if $f(x)=y$. When $f(x)=5$, $x=-7$, so $f^{-1}(5)=-7$

Step3: Find $f^{-1}(3)$

When $f(x)=3$, $x=5$, so $f^{-1}(3)=5$

Step4: Substitute values into expression

$$\begin{align*} f(3)-f^{-1}(5)-2f^{-1}(3)&=9-(-7)-2\times5\\ &=9+7-10 \end{align*}$$

Step5: Calculate final result

$9+7-10=6$

Answer:

$6$