Question

let $f(x)$ be a function with inverse $f^{-1}(x)$. the table below shows values of the function for selected values of $x$ in its domain.

$x$

$f(x)$

----

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$-4$

$-8$

$-2$

$-4$

$-1$

$0$

$0$

$1$

$1$

$3$

$4$

$6$

based on this table, what is the value of $f^{-1}(-4)$?

a. $-8$
b. $-2$
c. $4$
d. $6$

Explanation:

Step1: Recall inverse function definition

For inverse functions, if $f(a) = b$, then $f^{-1}(b) = a$.

Step2: Find $x$ where $f(x)=-4$

From the table, when $x=-2$, $f(-2) = -4$.

Step3: Apply inverse function rule

Since $f(-2) = -4$, then $f^{-1}(-4) = -2$.

Answer:

B. -2