Question

State if the given functions is an inverse. f(x)=2-1/2x, h(x)=-2x+4

Answer 1

Answer:

Not inverse between each other

Step-by-step explanation:

To determine if two mathematical functions are inverse between each other, you should verify that: for function f(x) and h(x)

- f(h(x)) = x for all and each x within h domain

- h(f(x)) = x for all and each x within f domain

So we should verify that we will obtain the same result when doing f(h(x)) and h(f(x)), if so, then both function are inverse between each other

f(x) = (2-1)/2x                                                                                                    h(x) = -2x + 4

f(h(x)) = (2-1)/2(-2x+4)                                                                                    h(f(x)) = -2[(2-1)/2x] + 4

f(h(x)) = (2-1)/-4x+8                                                                                         h(f(x)) = [(-4+2)/2x] + 4

f(h(x)) = (2-1)/8-4x                                                                                           h(f(x)) = (-4+2+8x)/2x

                                                                                                                            h(f(x)) = (8x-2)/2x                                                                                                                              

As we finally found that f(h(x)) ≠ h(f(x)), so both functions are not inverse between each other