Question

Find the domain and range of f(x)= 1+ cos2x .

Answer 1

Final Answer :
Range :
$0 \leqslant f(x) \leqslant 2$
Domain:
$0 \leqslant x \leqslant \frac{\pi}{2}$
Here, we are bounding our trigonometric function up-to priciplal values only.


So,
We know that

$- 1 \leqslant \cos(x) \leqslant 1 \\ = > - 1 \leqslant \cos(2x) \leqslant 1$

So,
f(x) = 1 + cos(2x)
Then,
$1 - 1 \leqslant f(x) \leqslant 1 + 1 \\ = > 0 \leqslant f(x) \leqslant 2$

Since, we are bounding our domain up-to principal values only.
$0 \leqslant 2x \leqslant \pi \\ = > 0 \leqslant x \leqslant \frac{\pi}{2}$