# How do you find the domain & range for f(x) = 2cos(4x + pi) -1 ?

Nov 14, 2015

DOMAIN

The domain of definition of a function is represented by points on the x-axis where the function is defined.
Here, the function $f \left(x\right)$ is defined for all real values of x, and hence the domain is the set of real numbers.

RANGE

The range of any cosine function (regardless of its argument) is $\left[- 1 , 1\right]$

Thus the range for this function is:

$\left[2 \cdot \left(- 1\right) - 1 , 2 \cdot \left(1\right) - 1\right]$

$= \left[- 3 , 1\right]$