For the functions f(x) = (x - 3)^2 - 2 and g(x) = |3x - 10|, what is the value of the comp… — ACT

For the functions $f(x) = (x - 3)^2 - 2$ and $g(x) = |3x - 10|$ , what is the value of the composite function $g(f(1))$ ?

The correct answer is 4

Evaluating

f(1)

gives

(1 - 3)^2 - 2 = (-2)^2 - 2 = 4 - 2 = 2

. Substituting this result into

g(x)

gives

g(2) = |3(2) - 10| = |6 - 10| = |-4| = 4

. Therefore, the value of the composite function is 4.

Evaluate the inner function

f(x)

x = 1

f(1) = (1 - 3)^2 - 2 = (-2)^2 - 2 = 4 - 2 = 2

To evaluate the composite function

g(f(1))

, the output of the inner function

f(1)

must be calculated first.

Substitute the output

f(1) = 2

into the outer function

g(x)

g(2) = |3(2) - 10| = |6 - 10| = |-4| = 4

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

g(x)

Evaluating a composite function by first calculating the value of the inner function and then using that result as the input for the outer function.

Estimated Time:1m 0s

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