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Given that f(x) = 3x – 5 and g(x) = x3 – x, what is f(g(2))?
Title
Composition with Cubic
Your Result
Correct
Difficulty
Medium
Your Pace
0:01
Others' Pace
0:44
Note: This Math prompt was developed prior to the Enhanced ACT and you may see an extra answer choice referenced in the explanation. The problem solving approach is still valid and you can ignore references to the extra answer choice.
Video Explanation
Text Explanation
Since g(x) is inside f(x), we first have to plug x = 2 into g(x), and then the output of g(2) will be the input of f(x).
g(x) = x3 – x
g(2) = (2)3 – 2 = 8 – 2 = 6
That's the output of g(2), so that's what we plug into f(x).
f(g(2)) = f(6) = 3(6) – 5 = 18 – 5 = 13
Answer = (D)
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