Hello. I need immediate help with my math homework. Please help me as soon as possible please

Question

A.)

B.)

C.)

D.)

Please help me by explaining and solving

Answer 1

g(f(x)) means you put f(x) into g(x)

for example if we were to do g(3) we'd replace the x in g with a 3. So we'd get g(3) = √(3 - 3) = 0

but for this problem instead of plugging in some number into g, we're putting in an entire function

so put f(x) = x² - 1 into g(x) by replacing the x with f(x), then simpify

the domain of g(f(x)) should be a range of x that keeps that function a real number, where the number under the square root stays positive

I recommend using Desmos or a graphing tool

Answer 2

in g(x) substitute g(x) which is x^2 -1 for x so,you,get

sqroot x^2-1 -3= x^2-4 so,g(f(x)= sqroot (x^2-4)

since you can’t get a square root for a negative number than mean X^2-4 >0 or x^2>4

so x >2 or less than-2

so answer is c