Question

If h(x) is the inverse of f(x), what is the value of h(f(x))?

Answer 1

$h(f(x))$ ⇒ $x$

Step-by-step explanation:

In mathematics, an inverse function is a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa, i.e., f(x) = y if and only if g = x.

Here we have , h(x) is the inverse of f(x) .We need to find the value of h(f(x)) . Let's find out:

Let inverse of $f(x)$  = $f^{-1}(x)$ , but according to question it's equivalent to h(x) i.e. $h(x) = f^{-1}(x)$ . Now,

$h(f(x))$

⇒ $h(f(x))$

putting value of f(x) in x at h(x) , i.e. $h(x) = f^{-1}(x)$

⇒ $f^{-1}(f(x))$

Multiplication of $f^{-1}$ and $f$ is 1 ,

⇒ $x$

Therefore, $h(f(x))$ ⇒ $x$ .