Perform the indicated operation and state the domain for f(g(x)) where [f(x)=4x^(-5)] and [g(x)=x^(3/4)] . Solution Given `f(x)=4x^(-5)` and `g(x)=x^(3/4)` find `f(g(x))` and state the domain. (1) `f(g(x))=4(x^(3/4))^(-5)` `=4(x^(-15/4))` `=4/(x^(15/4))` (2) The domain is `x>0` . We cannot divide by zero, so `x != 0` . Also we are taking an even root, so in the reals `x > 0` . (3) `g(f(x))=(4x^(-5))^(3/4)` `=4^(3/4)x^(-15/4)` `= (4^(3/4))/(x^(15/4))` Here the domain is also x>0..

1. Perform the indicated operation and state the domain for f(g(x)) where [f(x)=4x^(-5)] and
[g(x)=x^(3/4)] .
Solution
Given `f(x)=4x^(-5)` and `g(x)=x^(3/4)` find `f(g(x))` and state the domain.
(1) `f(g(x))=4(x^(3/4))^(-5)`
`=4(x^(-15/4))`
`=4/(x^(15/4))`
(2) The domain is `x>0` . We cannot divide by zero, so `x != 0` . Also we are taking an even
root, so in the reals `x > 0` .
(3) `g(f(x))=(4x^(-5))^(3/4)`
`=4^(3/4)x^(-15/4)`
`= (4^(3/4))/(x^(15/4))`
Here the domain is also x>0.