answer:
(a) To find the composite function fog, we substitute g(x) into f(x).
fog = f(g(x))
= f(x^2)
= 5(x^2) + 5
= 5x^2 + 5
The domain of fog is all real numbers since there are no restrictions on the domain of the original functions f(x) and g(x).
(b) To find the composite function gof, we substitute f(x) into g(x).
gof = g(f(x))
= g(5x + 5)
= (5x + 5)^2
= 25x^2 + 50x + 25
The domain of gof is all real numbers since there are no restrictions on the domain of the original functions f(x) and g(x).
(c) To find the composite function fof, we substitute f(x) into f(x).
fof = f(f(x))
= f(5x + 5)
= 5(5x + 5) + 5
= 25x + 30
The domain of fof is all real numbers since there are no restrictions on the domain of the original function f(x).
(d) To find the composite function g0g, we substitute g(x) into g(x) but replace x with 0.
g0g = g(g(0))
= g(0^2)
= g(0)
= 0^2
= 0
The domain of g0g is all real numbers since there are no restrictions on the domain of the original function g(x).
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