Question

A function is defined as shown.f(x)=−3x+4What is the inverse of f(x)?

Answer 1

Answer:
`f^(-1)(x)\text{ = -}(1)/(3)x\text{ + }(4)/(3)\text{ \lparen third option\rparen}`

Step-by-step explanation:

Given:

f(x) = -3x + 4

To find:

the inverse of the function

To determine the inverse, let y = -3x + 4

interchange x and y:

`x\text{ = -3y + 4}`

Solve for y by making it the subject of formula:

`\begin{gathered} subtract\text{ 4 from both sides:} \\ x\text{ - 4 = -3y + 4 - 4} \\ x\text{ - 4 = -3y} \end{gathered}`

divide both sides by -3:

`\begin{gathered} \frac{x\text{ - 4}}{-3}\text{ = }(-3y)/(-3) \\ y\text{ = }\frac{x\text{ - 4}}{-3} \\ y\text{ = }(x)/(-3)\text{ -}(4)/(-3) \end{gathered}`
`\begin{gathered} y\text{ = }(-x)/(3)\text{ + }(4)/(3) \\ \\ y\text{ = -}(1)/(3)x\text{ + }(4)/(3)\text{ } \\ \\ f^(-1)(x)\text{ = -}(1)/(3)x\text{ + }(4)/(3)\text{ \lparen third option\rparen} \end{gathered}`