Answer:
[tex]y=0.5x+2[/tex]
Step-by-step explanation:
Finding the inverse of a function is essentially finding the complete opposite of a given function. An easy trick can be used to find the inverse of a function. This trick is essentially thinking of the evaluator (f(x)) as another variable. Solve the function for (x) in terms of (f(x)); use inverse operations to do so. After completing this process, rewrite the function such that it is in the inverse function notation; switch the position of the (f(x)) and the (x), then indicate that it is an inverse function.
[tex]f(x)=2x-4[/tex]
Inverse operations,
[tex]f(x)=2x-4[/tex]
[tex]f(x)+4=2x[/tex]
[tex]\frac{f(x)+4}{2}=x[/tex]
Simplify,
[tex]0.5f(x)+2=x[/tex]
Rewrite in inverse function notation,
[tex]f^-^1(x)=0.5x+2[/tex]
[tex]y=0.5x+2[/tex]
