Question

someone please help medal award!

Given f(x)=x^2-3 and g(x)=x+2, find the following (write in general form).

a) f(g(x))
b) g(f(x))
c. f(f(x))
d. evaluate f(g(-5))

Answer 1

Okay so first things first. Put g(x) inside the f(x) equation.

Answer 2

For a)

Answer 3

would I have to multiply x^2-3 by x+2? for a?

Answer 4

\[(x+2)^2 -3\]

Answer 5

you replace the x from f(x) with the equation of g(x)

Answer 6

oh i see I got x^2+4x+1

Answer 7

Correct

Answer 8

You do basically the opposite for B)

You use the g(x) equation and replace the x with the f(x) equation

Answer 9

but how would you set it up since theres a -3 and a 2?

Answer 10

You replace X with (X^2 -3) +2

Answer 11

+2 is from g(x) = x "+2"

Answer 12

I got X^2-1

Answer 13

and for f I believe it's set up as (x^2-3)-3

Answer 14

for f(f(x))?

Answer 15

the X^2-1 I got for problem b I simplified it, and I set up (x^2-3)+2 for problem c

Answer 16

and for f I set it up as g(-5)=(-5+2)^2-3

Answer 17

Yes for B that is correct, But for c) you use f(f(x)). You do not use g(x) in the question.

Answer 18

so for c it would be (x^2-3)(x^2-3)?

Answer 19

\[f(f(x)) = (x^2 - 3)^2-3\]

Answer 20

and c factors out to x^4-6x^2+6 :)

Answer 21

Correct! :)

Answer 22

thanks so much :-) for d I got 6 I wasn't sure if I set it up correctly I set it up as (-5+2)^2-3

Answer 23

That's what I got too, and np! :)

Answer 24

thanks so much for all your help :D