How do you find the domain and range of $3 - cos 2 x$ $3-cos2x$ ?

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Answer 1 · 2017-08-05T13:22:48

Domain: $(- \infty, + \infty)$ $(-oo, +oo)$
Range: $[4, 2]$ $[4,2]$

$f (x) = 3 - cos 2 x$ $f(x) = 3-cos2x$

$f (x)$ $f(x)$ is defined $forall x in RR$

Hence, the domain of $f(x) = (-oo, +oo)$

Let $theta =2x$

$:. f(x) = 3-costheta$

The range of $cos theta =+-1$

$:.$ the range of $f(x) = [3+1, 3-1] = [4,2]$

This can be see from the graph of $f(x)$ below.

graph{3-cos(2x) [-10.21, 9.79, -1.76, 8.24]}

How do you find the domain and range of 3-cos2x3−cos2x3-cos2x?