Question

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

Answer 1

1/3(x+5)

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

`f^(-1)(x)=(x+5)/(3)`

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.}`

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

`\mathrm{Switch \: variables.}`

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

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

`f^(-1)(x)=(x+5)/(3)`