Mark the correct alternative in each of the following:
If f : R → (–1, 1) is defined by then f^–1(x) equals

Question

Mark the correct alternative in each of the following: If f : R → (–1, 1) is defined by then f –1 (x) equals

Philoid · Accepted Answer

Given that f : R → (–1, 1) is defined by

Here for mod function we will consider three cases, x = 0, x<0 and x>0.

For x< 0

⇒ y(1 + x²) = x²

⇒ x² (1 – y) = y

Also, checking on x>0 and x = 0 we find that

Mark the correct alternative in each of the following:If f : R → (–1, 1) is defined by then f–1(x) equals