Question

If f(x) = x³ + x - 5 and g(x) be another function such that g(f(x))  =x then find the value of g'(63)

(1) \(\frac1{50}\)

(2) \(\frac1{49}\)

(3) \(\frac1{48}\)

(4) \(\frac1{47}\)

Answer 1

Correct option is (2) \(\frac1{49}\) 

\(g' (f(x)) = \frac1 {f'(x)}\)   .....(1)

to find g'(63) put f(x) = 63

x³ + x - 5 = 63

x(x² + 1) = 68

⇒ x = 4

Now f'(x) = 3x² + 1

⇒ f'(4) = 49

then the value of g'(63) = \(\frac1{49}\)