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Difficulty: EasyFunction Evaluation, Composition, and Properties

If f(x)=3x−5f(x) = 3x - 5 and g(x)=(x−1)2g(x) = (x - 1)^2, what is the value of f(g(4))f(g(4))?

  1. A
    4
  2. B
    12
  3. 22Answer
  4. D
    36
  5. E
    40

Answer

22
To find f(g(4))f(g(4)), we evaluate the inner function first: g(4)=(4−1)2=32=9g(4) = (4 - 1)^2 = 3^2 = 9. We then evaluate the outer function at this result: f(9)=3(9)−5=27−5=22f(9) = 3(9) - 5 = 27 - 5 = 22.

Step-by-Step Solution

1
Evaluate the inner function g(x)g(x) at x=4x = 4
g(4)=(4−1)2=32=9g(4) = (4 - 1)^2 = 3^2 = 9
In function composition f(g(x))f(g(x)), the inner function must be evaluated first.
2
Substitute the result from the first step into the outer function f(x)f(x)
f(9)=3(9)−5f(9) = 3(9) - 5
The output of the inner function becomes the input of the outer function.
3
Calculate the final value of f(9)f(9) following the order of operations
f(9)=27−5=22f(9) = 27 - 5 = 22
Multiplication must be performed before subtraction.

Key Concept

Function Evaluation and Composition
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Topics

Function Evaluation, Composition, and Properties

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