Question Detail

MTH 102 MTH 102 Past Questions Objective Question
Take CBT

Question

Given the functions f(x) = 3x² – 2x + 1 and g(x) = 2x + 5, evaluate g(f(x)).
Options
A <code>2x² + 3x</code>
B <code>6x² - 4x + 7</code>
Correct Answer
C <code>2x² + 2x + 71</code>
D <code>2x² - 3x + 1</code>
Correct Answer

Option B is the correct answer.

Detailed Explanation

To evaluate the composite function g(f(x)):
  1. Substitute f(x) into g(x):g(f(x)) = g(3x² - 2x + 1)
  2. Replace x in the definition of g(x) with 3x² - 2x + 1:g(f(x)) = 2(3x² - 2x + 1) + 5
  3. Distribute and simplify:g(f(x)) = 6x² - 4x + 2 + 5g(f(x)) = 6x² - 4x + 7
This matches option B.

Hint

Remember that g(f(x)) means to first apply the function f to x, and then apply the function g to the result of f(x).

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 435 of 930
Previous Course Details Next