Question

What is the inverse of the function `f(x) = x +3`?

Answer 1

`f^(-1)(x)=x-3`

Explanation:

To find the inverse of a function, just "trade" `x` and `y` and solve for the "new" `y`. The graph of the inverse is the reflection of the original function over the line `y=x`.

Rewrite the function `f(x)=x+3`

as the equation `y=x+3`

Trade `x` and `y`.

`x=y+3`

Solve for the "new" `y`.

`xcolor(white)(aaa)=y+3`
`color(white)(a)-3color(white)(a^2aa)-3color(white)(aaa)`Subtract 3 from both sides

`x-3=y`

`y=x-3`

The symbol for the inverse is `f^(-1)(x)`

`f^(-1)(x)=x-3`