Question

Sekkrit!!! Find the inverse of f(x) = 3x-5

Answer 1

Answer:

1/3(x+5)

Step-by-step explanation:

f(x) = 3x-5

y = 3x-5

Exchange x and y

x = 3y-5

Solve for y

Add 5 to each side

x+5 = 3y

Divide each side by 3

1/3 ( x+5) = 3y/3

1/3 ( x+5) = y

The inverse is 1/3(x+5)

Answer 2

Answer:

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

Step-by-step explanation:

$f(x)=3x-5$

$\mathrm{We \: need \: to \: find \: the \: inverse \: of \: the \: function.} \\ \mathrm{The \: inverse \: of \: a \: function \: reverses \: the \: original \: function.}$

$\mathrm{Plug \: f(x) \: as \: y.}$

$y=3x-5$

$\mathrm{Solve \: for \: x.}$

$\mathrm{Add \: 5 \: to \: both \: sides \: of \: the \: equation.}$

$y+5=3x$

$\mathrm{Divide \: both \: sides \: of \: the \: equation \: by \: 3.}$

$\frac{y+5}{3} =x$

$\mathrm{Switch \: variables.}$

$\frac{x+5}{3} =y$

$\mathrm{Plug \: y \: as \: f^{-1}(x).}$

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