if f(x)=x^2-25 and g(x)=square root x then find g(f(x)) and its domain

Answer 1

f(x) = x^2-25

g(x) = sqrx

g(f(x) = g(x^2-25) = sqr(x^2 -25)

domain is any real number except -5 < x < 5 as that would make the square root of a negative number

Answer 2

I wish Wyzant Ask An Expert supported LaTeX....

g(f(x)) = √(x² - 25) that is, everything under the square root

so x² ≥ 25 or, x ≤ -5 or x ≥ 5