Question

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

X-
F(x) = -1
o ft (x) = 1 / 2 - 2 / 2
Of(x) = -2x + 3
Of(x) = 2x+ 3

Answer 1

`\displaystyle f^(-1)(x)=(x-3)/(2)`

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=(y-3)/(2)`

* Swap the variables:

`\displaystyle y=(x-3)/(2)`

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

`\mathbf{\displaystyle f^(-1)(x)=(x-3)/(2)}`