Let f : R [] R be defined as f(x) = x^3 + x - 5.

Question

Let f : R $$\to$$ R be defined as $f(x) = {x^3} + x - 5$. If g(x) is a function such that $$f(g(x)) = x,\forall 'x' \in R$$, then g'(63) is equal to \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.

Accepted Answer

$f(x) = 3{x^2} + 1$

f'(x) is bijective function

and $$f(g(x)) = x \Rightarrow g(x)$$ is inverse of f(x)

$g(f(x)) = x$

$$g'(f(x))\,.\,f'(x) = 1$$

$$g'(f(x)) = {1 \over {3{x^2} + 1}}$$

Put x = 4 we get

$$g'(63) = {1 \over {49}}$$

Solutions · 1