Answer:
[tex]f^{-1}(x)=-\frac{1}{12}x+\frac{1}{2}[/tex]
Step-by-step explanation:
* Lets explain how to find the inverse function
- If f(x) = y, then its inverse is [tex]f^{-1}(x)[/tex]
- 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 [tex]f^{-1}[/tex] 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
∴ [tex]y=\frac{x}{-12}-\frac{6}{-12}[/tex]
- Remember x/-12 is the same as (-1/12)x and (-)(-) = (+)
∴ [tex]y=-\frac{1}{12}x+\frac{1}{2}[/tex]
∴ [tex]f^{-1}(x)=-\frac{1}{12}x+\frac{1}{2}[/tex]
