Question

F(x)=-12x+6, then f-1(x)=?

Answer 1

`f^(-1)(x)=-(1)/(12)x+(1)/(2)`

Explanation:

* Lets explain how to find the inverse function

- If f(x) = y, then its inverse is
`f^(-1)(x)`

- To find the inverse function we switch x and y and solve to find the

new y

- The domain of the function f(x) = y is x and its range is y

- The domain of
`f^(-1)` is y and its range is x

* Lets solve the problem

∵ f(x) = -12x + 6

∵ f(x) = y

∴ y = -12x + 6

- Lets switch x and y to find the inverse of f(x)

∵ y = -12x + 6

∴ x = -12y + 6

- Lets solve for y

∵ x = -12y + 6

- Subtract 6 from both sides

∴ x - 6 = -12y

- Divide both sides by -12

∴
`y=(x)/(-12)-(6)/(-12)`

- Remember x/-12 is the same as (-1/12)x and (-)(-) = (+)

∴
`y=-(1)/(12)x+(1)/(2)`

∴
`f^(-1)(x)=-(1)/(12)x+(1)/(2)`