Hello I’m new to wyzant. Please help me with my Algebra homework as soon as possible please I am so stressed.

Question

1.

  A.)

B.)

C.)

D.)

2.)

A.)

B.)

C.)

D.)

Please help me by explaining and solving

Answer 1

1. f(x)=2x²-1. g(x)=√(x-2).

f(g(x)) is read "f of g of x", and it means to put the g(x) function in for x into the f(x) function. So:

f(√(x-2))=2(√(x-2))²-1.

Since squaring and taking a square root are inverse operations, they cancel out, and f(√(x-2))=2(x-2)-1.

2(x-2)-1=2x-4-1=2x-5.

You're given the domain x≥2, which is also the domain of the final function. Technically, if it weren't a composite function with the radical as part of the composition, the domain would be all real numbers. However, we cannot have a negative number under a square root sign, so x has to be at least 2. The final domain, given the original composition, should also be x≥2.

I'm not doing your whole assignment here, but if you need help understanding it, get in touch! Also, maybe this one will help you progress on the others.

I hope this helps, and take care!

Liz Z.