What is the inverse of the function f(x) = 4x + 8?

Solution:

If the composition of two functions results in an identity function (I(x) = x), then the two functions are said to be inverses of each other.

The inverse of a function f is denoted by f^-1 and it exists only when f is both one-one and onto function.

Note that f^-1 is NOT the reciprocal of f.

In the given function, let f(x) = y

4x + 8 = y

⇒ 4x = y - 8

⇒ x = (y - 8)/4 --- (1)

Now if f(x) = y , then x = f⁻¹(y) --- (2) substitute (2) in (1)

f⁻¹(y) = (y - 8)/4

⇒ f⁻¹f(x) = (x - 8)/4

Example: What is the inverse of the function f(x) = 5x - 7?

Let f(x) = y

5x - 7 = y

⇒ 5x = y + 7

⇒ x = (y + 7) / 5 --- (1)

Now if f(x) = y , then x = f⁻¹(y) --- (2)

Substitute (2) in (1)

f⁻¹(y) = (y + 7) / 5

⇒ f⁻¹(x) = (x + 7) / 5

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What is the inverse of the function f(x) = 4x + 8?

Summary:

The inverse of the function f(x) = 4x + 8 is f⁻¹(x) = (x - 8)/4