Domain and Range Question 2

For the functions $f(x)=4x+12$ and $g(x)=\dfrac{1}{x}$ , what is the set of real numbers $x$ on which $g(f(x))$ is defined?

All real numbers

All real numbers except

3

All real numbers except

0

All real numbers except

-\dfrac{1}{3}

All real numbers except

-3

Approach

g(f(x)) = \frac{1}{4x+12}

This composite function is undefined when the denominator is $0$ .

4x+12 \neq 0

4x \neq -12

x \neq \boxed{-3}