The answer (g(x))=x−7
g(f(x))=√x2−7
Explanation:
Put g inside f to find f(g(x))
f(x)=x2−4
g(x)=√x−3
f(g(x))=(√x−3)2−4
f(g(x))=x−3−4
f(g(x))=x−7
Put f inside g to find g(f(x))
g(x)=√x−3
f(x)=x2−4
g(f(x))=√x2−4−3
g(f(x))=√x2−7:
The answers are f(g(x))=x−7
and g(f(x))=√x2−7
Explanation:
This is a composition of functions.
f(x)=x2−4
g(x)=√x−3
fog(x)=f(g(x))=f(√x−3)=(√x−3)2−4
=x−3−4=x−7
And
gof(x)=g(f(x))=g(x2−4)=√(x2−4)−3
=√x2−4−3=√x2−7
You can see that
f(g(x))≠g(f(x))
