Question

evaluate functions and inverses from tables (level 2)
score: 0/1 penalty: none
question
find $5g^{-1}(f(-16)) - g^{-1}(-14)$.

$x$

$f(x)$

$g(x)$

-----

--------

--------

3

13

8

$-7$

19

20

$-16$

$-12$

$-5$

8

7

4

13

4

$-14$

$-12$

2

$-12$

4

$-14$

$-15$

answer attempt 1 out of 3

Explanation:

Step1: Find $f(-16)$

From the table, when $x=-16$, $f(x)=-12$, so $f(-16)=-12$.

Step2: Find $g^{-1}(-12)$

$g^{-1}(y)$ is the $x$ where $g(x)=y$. When $g(x)=-12$, $x=-12$, so $g^{-1}(f(-16))=g^{-1}(-12)=-12$.

Step3: Find $g^{-1}(-14)$

When $g(x)=-14$, $x=13$, so $g^{-1}(-14)=13$.

Step4: Calculate the expression

Substitute values into $5g^{-1}(f(-16)) - g^{-1}(-14)$:
$5\times(-12) - 13 = -60 -13$

Answer:

$-73$