Only question i'm unsure of..

f(x)=6-x²

g(x)=1/(x+2)

k(x)=√x

determine an explicit equation for p(x)=g(f(x)) + k(x), then state its domain.


Here's what i have worked up so far.

6-x² into g = 1/(6-x²)+2
=1/8-x² + k(x)

=1/8-x² + √x

1) fix your parenth
2) to help check your answer, pick a value for x, then compute it numerically and do the compositions, then compare it to your final result.

set it equal to 0 and solve for x?

Your work looks correct so far. Now to find the domain, find all values of x that would make the composite function undefined or imaginary (ex sqrt(x) with x<0)

=1/8-x² + √x

Domain:

8-x² = 0
x² = 8
x = +2√2 or x = -2√2

So, domain can be any value different from + or - 2√2.

This post was edited by betoggc on Sep 26 2014 09:36am

no negative under square root

Correct!

Forgot to mention it