Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

Given the functions f(x) = 3x²-5, 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 expression for g(x) into f(x):f(g(x)) = f(5x-1)Substitute (5x-1) for x in f(x) = 3x² - 5:f(5x-1) = 3(5x-1)² - 5First, expand (5x-1)²:(5x-1)² = (5x)² - 2(5x)(1) + 1² = 25x² - 10x + 1Now substitute this back:f(5x-1) = 3(25x² - 10x + 1) - 5= 75x² - 30x + 3 - 5= 75x² - 30x - 2. This matches option A.

Hint

To find f(g(x)), substitute the entire expression for g(x) into every instance of 'x' in the definition of f(x), then simplify.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 262 of 930
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