Hi
f(x) and h(x) are inverses of one another:
f(x)=X+5/2 | y = x + 5/2 Exchange: x = y + 5/2 0r y = x-5/2 0r checks.
h(x)=x-2/5 |y = x-2/5 EXCHANGE: x = y-2/5 0r y = x + 2/5 0r checks.
Wish You the Best in your Studies.
None of the functions are inverses of each other. Don't be confused by the absurd response from the other tutor, in which she says that f^-1(x)=x-5/2 and that is equal to h(x), which is x-2/5. The way I learned math, 5/2 and 2/5 are not the same....
I would never find the inverses of these functions using the formal process of switching the x and y and solving for the new y.
All of these functions are simple enough that you can find the inverses using the concept that the inverse function "un-does" what the function does.
f(x)= x+5/2: the rule for the function is "add 5/2"; the rule for the inverse is "subtract 5/2". f^-1(x) = x-5/2.
g(x) = 2x+5: the rule for this function is "multiply by 2 then add 5"; the rule for the inverse is "subtract 5 and then divide by 2". g^-1(x) = (x-5)/2.
h(x) = x-2/5: the rule for this one is "subtract 2/5"; the rule for the inverse is "add 2/5". h^-1(x) = x+2/5.
None of the functions has an inverse that is one of the other functions....