Let f : R → R be the function defined by . Then, find the range of f.

Question

Philoid · Accepted Answer

We have,

Let

⇒ 2y–ycosx = 1

⇒ -ycosx = 1-2y

⇒

Now, we know that range of cosx is [-1,1].

⇒ -1 ≤ cosx ≤ 1

⇒

On multiplying the inequality by -1 we get,

⇒

Note : The sign of inequality is reversed if it is multiplied by a negative quantity.

⇒

Thus, range of