Q43 of 215 Page 3

Mark the correct alternative in each of the following:

If f : R → (–1, 1) is defined by then f–1(x) equals


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


More from this chapter

All 215 →
41

Mark the correct alternative in each of the following:

The distinct linear functions which map [–1, 1] onto [0, 2] are


 42

Mark the correct alternative in each of the following:

Let f : [2, ∞) → X be defined by f(x) = 4x – x2. Then, f is invertible, if X =


 44

Mark the correct alternative in each of the following:

Let [x] denote the greatest integer less than or equal to x. If f(x) = sin–1 x, g(x) = [x2] and then


 45

Mark the correct alternative in each of the following:

If g(x) = x2 + x – 2 and gof (x) = 2x2 – 5x + 2, then f(x) is equal to