The table below shows some values for the functions f and g. | x | f(x) | g(x) | |---|---|---| | -1 | 2 | 3 | | 0 | 1 | -1 | | 1 | -3 | 2 | | 2 | 0 | 1 | | 3 | -2 | 0 | What is the value of g(f(2))?

The table below shows some values for the functions f and g. | x | f(x) | g(x) | |---|---|… — ACT

The table below shows some values for the functions $f$ and $g$ .

What is the value of $g(f(2))$ ?

The correct answer is

-1

To find the value of

g(f(2))

, we begin with the inner function

f(2)

. Looking at the table, when

x = 2

, the value of

f(x)

0

. This means

f(2) = 0

. We then substitute this value into the outer function, giving us

g(0)

. Looking at the table again, when

x = 0

, the value of

g(x)

-1

. Therefore,

g(f(2)) = -1

Find the value of the inner function

f(2)

from the table.

f(2) = 0

For the composed function

g(f(2))

, the inner function

f

must be evaluated first at the input

2

Substitute this result into the outer function to evaluate

g(0)

using the table.

g(0) = -1

The output of the inner function becomes the input for the outer function

g

Evaluating composite functions using a table of values

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