Question

Let f (x) > 0 for all x and f '(x) exists for all x. If f is the inverse function of h and h'(x) = `1/(1 + logx)`. Then f'(x) will be ______ 

पर्याय

• 1 + log (f(x))

• 1 + f(x)

• 1 - log (f(x))

• log f(x)

Answer 1

Let f (x) > 0 for all x and f '(x) exists for all x. If f is the inverse function of h and h'(x) = `1/(1 + logx)`. Then f'(x) will be 1 + log (f(x)).

Explanation:

According to the given condition,

h (f(x)) = x

Differentiating w.r.t. x, we get

h'(f(x)) × f'(x) = 1

⇒ f'(x) = `1/(h^'(f(x)))`

⇒ f'(x) = 1 + log (f(x))