Looks good to me . . . Nice work!
I just want to check if i did these questions right, ym textbook doesn't have any examples of them, so there's no way for me to check
a) f(x) = sqrt(x+1)
g(x) = sqrt(x-1)
= sqrt(x+1) * sqrt(x-1)
= sqrt(x^2 - 1)
= sqrt(x+1) / sqrt(x-1)
= sqrt[(x+1)(x-1)] / x-1
First of all, I assume that which is the common logarithm.
Now it is obvious that
This is followed by the definition of logarithms:
If , then .
When we simply make the substitution in , we get .
We can also substitute in If when we get .
We also note that since and , f and g are each other's inverse functions.
By the way, do not forget about the range of definition when dealing with functions.