Question 976133
<font face="Times New Roman" size="+2">


Close.  You are making an error in WANTING to simplify *[tex \Large \left(\sqrt{x}\right)^4]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  h(x)\ =\ \sqrt{x}]


So


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  g(h(x))\ =\ \sqrt{x}\ -\ 4]


So


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  f(g(h(x)))\ =\ (\sqrt{x}\ -\ 4)^4\ +\ 6]


To simplify the 4th power binomial, use the binomial expansion:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (a\ +\ b)^4\ =\ a^4\ +\ 4a^3b\ +\ 6a^2b^2\ +\ 4ab^3\ + b^4]


and then substitute *[tex \Large \sqrt{x}] for *[tex \Large a] and *[tex \Large -4] for *[tex \Large b], doing all of the required arithmetic and being careful with your signs (even powers of negative numbers are positive, odd powers of negative numbers are negative).


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \