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Perform the indicated operation and state the domain for f(g(x)) where `f(x)=4x^(-5)`...

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Perform the indicated operation and state the domain for f(g(x)) where `f(x)=4x^(-5)` and `g(x)=x^(3/4)` .

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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.

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