Question

Find the inverse of the function.

f(x) = 5x + 6

Answer 1

f(x) = 5x + 6

let y = f(x)

y = 5x + 6    solving for x.

y - 6 = 5x

5x = y - 6

x = (y - 6)/5

Recall   f(x) = y.   Implies  x = f⁻¹(y)

x = (y - 6)/5

f⁻¹(y) = (y - 6)/5

So as well:

f⁻¹(x) = (x - 6)/5

Answer 2

The inverse of the function f(x) is $f^{-1}(x)=\frac{x-6}{5}$.

What is a inverse function?

The inverse function returns the original value for which a function gave the output. The inverse function of a function f is a function that undoes the operation of f.

For the given situation,

The function is f(x) = 5x + 6

let f(x) = y, then

$x = f^{-1}(y)$

Now substitute, $f^{-1}(y)$ in the place of x,

⇒ $y=5f^{-1}(y)+6$

⇒ $y-6=5f^{-1}(y)$

⇒ $f^{-1}(y)=\frac{y-6}{5}$

Now again interchange the function in terms of x,

⇒ $f^{-1}(x)=\frac{x-6}{5}$

Hence we can conclude that the inverse of the function f(x) is $f^{-1}(x)=\frac{x-6}{5}$.

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