Consider f: R → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.

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Solution

f: R → R is given by,

f(x) = 4x + 3

One-one:

Let f(x) = f(y).

∴ f is a one-one function.

Onto:

For y ∈ R, let y = 4x + 3.

Therefore, for any y ∈ R, there exists such that

∴ f is onto.

Thus, f is one-one and onto and therefore, f⁻¹ exists.

Let us define g: R→ R by.

∴

Hence, f is invertible and the inverse of f is given by

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