Question

Given g(x)=sqrt x-4 and h(x)=2x-8 what is (g(h(10)) HELP ME I AM .3 POINTS AWAY FROM PASSING.

Answer 1

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))

Answer 2

The answer is: X≥6

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