Question

Difficulty: EasyFunction Evaluation, Composition, and Properties

If $f(x) = 3x - 2$ and $g(x) = x^2 + 1$ , what is the value of $g(f(2))$ ?

Answer: 17

The value of

g(f(2))

is 17.

To evaluate the composite function

g(f(2))

, we first find the value of the inner function

f(2) = 3(2) - 2 = 4

. Then, we substitute this output as the input for the outer function to get

g(4) = 4^2 + 1 = 17

Substitute

x = 2

into the expression for

f(x)

to evaluate the inner function.

f(2) = 4

In the composition

g(f(2))

, the inner function

f(x)

must be evaluated first at the input value of 2.

Substitute the result from Step 1, which is 4, into the expression for

g(x)

g(4) = 17

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

g(f(2)) = g(4) = 4^2 + 1 = 17

Function Composition

Estimated Time:45s

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