5
lesson pretestMultiple Choice

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Question 5 • Math 3

Which statement describes the domain of the function f of x is equal to the fraction with numerator 3 x and denominator 4 x squared minus 4 ?

Answer
A
all nonzero real numbers
B
all real numbers
C
all real numbers except x is equal to 3 fourths
D
all real numbers except x is equal to negative 1 and x is equal to 1

Explanation

A rational function is undefined wherever its denominator equals zero. Solve 4x² − 4 = 0: factoring gives 4(x − 1)(x + 1) = 0, so x = 1 or x = −1. Excluding those values leaves all real numbers except −1 and 1, which is choice D.

AI-written and checked against the verified answer.

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