Question

Difficulty: EasyFunction Evaluation, Composition, and Properties

For the function $h(x) = 5 - 3x$ , what is the value of $h(h(2))$ ?

Answer: 8

To find

h(h(2))

, we first calculate the value of the inner function,

h(2) = 5 - 3(2) = 5 - 6 = -1

. We then substitute this result back into the function to evaluate the outer function:

h(-1) = 5 - 3(-1) = 5 + 3 = 8

. Therefore, the correct value is 8.

Evaluate the inner function

h(2)

h(2) = -1

To evaluate a nested function composition of the form

h(h(x))

, first calculate the value of the inner function at the given input.

Evaluate the outer function

h(-1)

using the result from Step 1

h(h(2)) = h(-1) = 8

Substitute the output of the inner function,

-1

, as the new input for the outer function

h(x)

Evaluating the composition of a function with itself

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