Timed! anyone know the answer to this algebra 2 problem?

C

Step-by-step explanation:

Choice A

Always start with the function on the far left of the combined function. So for Choice  A, you start with

g(a) = sqrt(a)

Now substitute the function on the right of the combined function into whatever you see on the right. In this question, f(a) goes on both sides of the combined function for a.

g(f(a)) = sqrt(f(a))

but f(a) = a^2 - 4

g(f(a)) = sqrt(a^2 - 4) You can't reduce this any further. A is not the answer.

Choice B

g(a) = 2a - 2       Put f(a) in for all a s

g(f(a)) = 2(f(a)) - 2 Now put in 1/2 a - 1 for f(a) on the right.

g(f(a)) = 2(1/2 a - 1) - 2

g(f(a)) = a - 2 - 2

g(f(a)) = a - 4 which is not the right result. B is not your choice.

Choice C

g(a) = sqrt(a - 5) - 2

g(f(a)) = sqrt( f(a) - 5 ) - 2

g(f(a)) = sqrt( 5 + a^2 - 5) - 2

g(f(a)) = sqrt(a^2) - 2

g(f(a)) = |a| - 2 which is the answer you should get.

the answer is c. 23/3