Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

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

Option A is the correct answer.

Detailed Explanation

To evaluate (f(g(x))), substitute (g(x)) into (f(x)).(f(g(x)) = f(5x-1))Now, replace (x) in (f(x)) with (5x-1):(f(5x-1) = 3(5x-1)^2 - 5)Expand the term ((5x-1)^2): ((5x-1)^2 = (5x)^2 - 2(5x)(1) + 1^2 = 25x^2 - 10x + 1).Substitute this back:(f(5x-1) = 3(25x^2 - 10x + 1) - 5)(= 75x^2 - 30x + 3 - 5)(= 75x^2 - 30x - 2).

Hint

Substitute the expression for \(g(x)\) into \(f(x)\) and simplify.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 241 of 930
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