Question

evaluate functions and inverses from tables (level 1)
score: 1/2 penalty: none
question
find $f(-4)-f^{-1}(-3).$

$x$

$f(x)$

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--------

$-4$

$-9$

$-17$

$8$

$-13$

$-4$

$4$

$7$

$11$

$-2$

$-9$

$-3$

Explanation:

Step1: Find $f(-4)$ from table

From the table, when $x=-4$, $f(x)=-9$, so $f(-4)=-9$.

Step2: Find $f^{-1}(-3)$

The inverse function $f^{-1}(y)$ gives the $x$ such that $f(x)=y$. When $f(x)=-3$, $x=-9$, so $f^{-1}(-3)=-9$.

Step3: Calculate the difference

Substitute the values into the expression: $f(-4)-f^{-1}(-3) = -9 - (-9)$

Answer:

$0$