Question

Which function is the inverse of f(x) = 2x + 3

Answer 1

Answer:

$\displaystyle f^{-1}(x)=\frac{x-3}{2}$

Step-by-step explanation:

The Inverse of a Function

The procedure to find the inverse of the function is:

* Write the function as a two-variable equation:

y = 2x + 3

* Solve the equation for x.

y - 3 = 2x

$\displaystyle x=\frac{y-3}{2}$

* Swap the variables:

$\displaystyle y=\frac{x-3}{2}$

Write back into function form. This is the inverse function:

$\mathbf{\displaystyle f^{-1}(x)=\frac{x-3}{2}}$