# How do you find the inverse of f(x)= 2x +3?

Mar 24, 2018

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

#### Explanation:

$y = f \left(x\right)$

$y = 2 x + 3$

Switch the places of $x$ and $y :$

$x = 2 y + 3$

Solve for $y :$

$2 y = x - 3$

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

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

Mar 24, 2018

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

#### Explanation:

Now, the inverse of a function is just writing $x$ in terms of $y$

So $f \left(x\right) = 2 x + 3$ becomes $y = 2 x + 3$

$y = 2 x + 3$ becomes $y - 3 = 2 x$

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

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

Finally just interchange x and y because we want the function in terms of x.
$y = \frac{x - 3}{2}$

So ${f}^{-} 1 \left(x\right) = \frac{x - 3}{2}$