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MTH 102 MTH 102 Past Questions Objective Question
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Question

Given the functions f(x) = 3x²-5 and g(x) = 5x-1, evaluate f(g(x)).
Options
A 75x² - 30x - 2
Correct Answer
B 25x² + 2x + 7
C 75x² + 3x +1
D 70x-70
Correct Answer

Option A is the correct answer.

Detailed Explanation

To evaluate f(g(x)), substitute the entire expression for g(x) into the function f(x).Given f(x) = 3x²-5 and g(x) = 5x-1.f(g(x)) = f(5x-1)Substitute (5x-1) for x in f(x):f(5x-1) = 3(5x-1)² - 5Expand the squared term (5x-1)² = (5x)² - 2(5x)(1) + 1² = 25x² - 10x + 1:f(5x-1) = 3(25x² - 10x + 1) - 5Distribute the 3:f(5x-1) = 75x² - 30x + 3 - 5Combine the constant terms:f(5x-1) = 75x² - 30x - 2.This matches option A.

Hint

When evaluating a composite function f(g(x)), replace every 'x' in the function f(x) with the entire expression for g(x).

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 257 of 930
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