college algebra word problem

Question

Use the pair of functions to find f(g(x)) and g(f(x)).

f(x) = x² + 9, g(x)= square root of x+2

Answer 1

Hello, thank you for taking the time to post your question!

f(g(x)) means plugging in g(x) into f(x)

f(sqrt(x+2)) = (sqrt(x+2))^2 + 9 = x + 2 + 9 = x + 11

then for g(f(x) you want to plug in f(x) into g(x)

g(x^2 + 9) = sqrt(x^2 + 9 + 2) = sqrt(x^2 + 11)

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

f(g(x)) = g(x)^2 + 9 = (x+2)^2 + 9 = x^2 +4x +13

g(f(x)) = sqr(f(x)) + 2 = sqr(x^2+9) + 2