Thread: f*g(x) and f/g(x) homework check

hey guys,
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)

f*g
= sqrt(x+1) * sqrt(x-1)
= sqrt[(x+1)(x-1)]
= sqrt(x^2 - 1)

f/g
= sqrt(x+1) / sqrt(x-1)
= sqrt[(x+1)(x-1)] / x-1

thanks

Hello, snypeshow!

Looks good to me . . . Nice work!

thanks!

I have another question that i'm having trouble with.

f(x) = 10^x
g(x) = log x

f(g(x)) = 10^logx
g(f(x)) = log (10^x)

how would i simplify f(g(x)) and g(f(x)) ?

First of all, I assume that which is the common logarithm.




Now it is obvious that
and


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.