How do you find the inverse of f(x)=3x-5?

Apr 17, 2018

$f {\left(x\right)}^{-} 1 = \frac{1}{3} x + \frac{5}{3}$

Explanation:

$f \left(x\right) = 3 x - 5$
The inverse of a function completely swaps the x and y values. One way to find the inverse of a function is to switch the "x" and "y" in a equation
$y = 3 x - 5$ turns into $x = 3 y - 5$
Then solve the equation for y
$x = 3 y - 5$
$x + 5 = 3 y$
$\frac{1}{3} x + \frac{5}{3} = y$
$f {\left(x\right)}^{-} 1 = \frac{1}{3} x + \frac{5}{3}$

Apr 17, 2018

$f \left(x\right) = 3 x - 5$

$y = 3 x - 5$

$x = 3 y - 5$

add three to both sides

$3 y = x + 5$

divide by $t h r e e$ on both sides

${f}^{-} 1 \left(x\right)$=$\frac{5}{3}$ + $\frac{x}{3}$

${f}^{-} 1 \left(x\right)$=$x + 5$ /$3$