Question

h(x)=(g o f)(x)=1/(x+3)^2 which of the following could be a possible decomposition of h(x)?
A. f(x)=1/x^2;g(x)=x+3
B. f(x)=x+3; g(x)=1/x^2
C.f(x)=x^2; g(x)=x+3
D. f(x)=1/x;g(x)=x+3

Answer 1

I think its C f(x)=x+3; g(x)=1/x^2

Because if you take f(x)=x+3 g(x)=1/x^2 plug the f(x) into the g(x) formula this is what you get g(x)=1/x^2 g(x)=1/(x+3)^2. I think

Answer 2

Do you mean B or C?

Answer 3

oh sorry I meant B

Answer 4

yeah,
f(x) = x+3, g(x) = 1/x^2
(g o f) (x) = 1/(x+3)^2.

Answer 5

What would you get with option A?

Answer 6

wouldn't that be (f o g)(x)

Answer 7

with A: f(x)=1/x^2; g(x)=x+3

fog would work to get the right result:
(f o g)(x) = f(x+3) = 1/(x+3)^2

But what would gof give?

Answer 8

(gof)(x) = g( f(x) )
= g( 1/x^2 )
= ?

Answer 9

wait so it would be (1/x^2)+3

Answer 10

that's correct

Answer 11

As we can now see B is the only correct option.

Answer 12

Right that's great. Thank you so much :)

Answer 13

\[\ddot\smile\]