Question

Which statement describes the domain of the function f (x) = StartFraction 3 x Over 4 x squared minus 4 EndFraction?

Answer 1

Answer: D on edge, all real numbers except x = –1 and x =

Step-by-step explanation:I took the test and its right.

Answer 2

The domain is the set of all real number except 1 and -1

Explanation:

We have the following function:

$f(x)=\frac{3x}{4x^2-4}$

So the domain is the set of all x-values for which the function is defined. Since we have $4x^2-4$ in the denominator, then:

$4x^2-4\neq 0 \\ \\ \\ Factor \ out \ 4: \\ \\ 4(x^2-1)\neq 0 \\ \\ (x^2-1)\neq 0 \\ \\ \\ Difference \ of \ squares: \\ \\ (x-1)(x+1)\neq 0 \\ \\ \\ So: \\ \\ \\\boxed{x\neq 1 \ and \ x\neq -1}$

In conclusion:

The domain is the set of all real number except 1 and -1

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