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

How do you find the domain & range for $f\left(x\right)=2\mathrm{cos}\left(4x+\pi \right)-1$?
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spornya1
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(x) 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 [-1,1]
Thus the range for this function is:
[2*(-1)-1,2*(1)-1]
=[-3,1]