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

Solution:

Given that h(x) is the inverse of f(x) then,

h[f(x)] = x

Consider F: A→B;

If there exists a function G: B →A such that G.F(x) = IA = x and F.G(y) = IB = y

Where,

IA and IB are identity functions on the domain of F and G respectively.

Then G is said to be the inverse function of F and vice versa.

Example:

Consider f: R→R defined by f(x) = 3x + 4 then there exists g:R→R defined by g(x) = (x - 4)/3 such that g(x) is the inverse of f(x)

g(f(x)) = g(3x + 4)

= (3x + 4 - 4)/3

= 3x/3

= x

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

Summary:

If h(x) is the inverse of f(x), then the value of h(f(x)) = x.