Find the domain and range of the function.
-$$f ( x ) = - 4 \cos ^ { 2 } x$$
A) Domain: $( - \infty , 0 ]$; range: $( - \infty , \infty )$
B) Domain: $( - \infty , \infty )$; range: $( - \infty , 0 ]$
C) Domain: $[ - 4,0 ]$; range: $( - \infty , \infty )$
D) Domain: $( - \infty , \infty )$; range: $[ - 4,0 ]$

Question

Quizplus · Accepted Answer

The domain of a cosine function is all real numbers $( - \infty , \infty )$ because cosine is defined for any real number. The range of $\cos^2x$ is $[0,1]$ because the square of cosine values (which range from -1 to 1) will be between 0 and 1. Multiplying by -4 shifts and scales this range to $[-4,0]$, but does not affect the domain.

Find the Domain and Range of the Function f(x)=−4cos⁡2xf ( x ) = - 4 \cos ^ { 2 } xf(x)=−4cos2x

Find the Domain and Range of the Function $f ( x ) = - 4 \cos ^ { 2 } x$