[tex]h(f(x))[/tex] ⇒ [tex]x[/tex]
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 [tex]f(x)[/tex] = [tex]f^{-1}(x)[/tex] , but according to question it's equivalent to h(x) i.e. [tex]h(x) = f^{-1}(x)[/tex] . Now,
[tex]h(f(x))[/tex]
⇒ [tex]h(f(x))[/tex]
putting value of f(x) in x at h(x) , i.e. [tex]h(x) = f^{-1}(x)[/tex]
⇒ [tex]f^{-1}(f(x))[/tex]
Multiplication of [tex]f^{-1}[/tex] and [tex]f[/tex] is 1 ,
⇒ [tex]x[/tex]
Therefore, [tex]h(f(x))[/tex] ⇒ [tex]x[/tex] .
