SOLUTION: Find (a) (f o g)(x) and the domain of f o g and (b) (g o f)(x) and the domain of g o f. the Square root symbol is across the whole equation if its not showing on the problem. f(x

Algebra ->  Rational-functions -> SOLUTION: Find (a) (f o g)(x) and the domain of f o g and (b) (g o f)(x) and the domain of g o f. the Square root symbol is across the whole equation if its not showing on the problem. f(x      Log On


   

Question 231790: Find (a) (f o g)(x) and the domain of f o g and (b) (g o f)(x) and the domain of g o f.
the Square root symbol is across the whole equation if its not showing on the problem.
f(x)= √25-x^2, g(x)=√x-3

I know how to do f o g and g o f, but I'm not sure how to work it out with square roots,
Thanks for your time.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find
(a) (f o g)(x) and the domain of f o g
fog(x) = f[sqrt(x-3)] = [25 -(x-3)] = [28-x]
Domain: All Real Numbers >= 3.
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(b) (g o f)(x) and the domain of g o f.
gof(x) = g[sqrt(25-x^2] = sqrt[sqrt(25-x^2)-3]
Domain: All Real Numbers x where -5<= x <= 5
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the Square root symbol is across the whole equation if its not showing on the problem.
f(x)= sqrt(25-x^2), g(x)= sqrt(x-3)
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Cheers,
Stan H.