Question

Which statement describes the domain of the function f (x) = StartFraction 3 x Over 4 x squared minus 4 EndFraction?
all real numbers
all nonzero real numbers
all real numbers except x = Three-fourths
all real numbers except x = –1 and x = 1

Answer 1

Answer:

D

Step-by-step explanation:

i just used desmos, never touches x=1 or x=-1

Answer 2

The domain of a function is the set of x values for which it is defined. The correct option is D.

What is the domain and range of a function?

The domain of a function is the set of x values for which it is defined, whereas the range is the set of y values for which it is defined.

To find the domain of the function it needed to be simplified. Therefore, the function can be rewritten as,

$f(x) = \dfrac{3x}{4x^2-4}\\\\f(x) = \dfrac{3x}{4(x^2-1)}$

As it can be seen that for the fraction of the value of x is kept -1 or 1, then the denominator of the function will become zero, which is undefined.

Hence, the domain of the given function is all real numbers except x = –1 and x = 1.

Learn more about Domain and Range:

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