Question

Find f(x) and g(x) so that the function can be described as y = f(g(x)).

y =(4/x^2) + 9

Answer 1

I think that a possible choice, can be this:
\[\begin{gathered}
g\left( x \right) = {x^2} \hfill \\
f\left( x \right) = \frac{4}{x} + 9 \hfill \\
\end{gathered} \]

Answer 2

we have:
\[\Large f\left( {g\left( x \right)} \right) = \frac{4}{{g\left( x \right)}} + 9 = ...?\]

Answer 3

my choices are
A.f(x)= x+9 g(x)= 4/x^2
B.f(x)= x g(x)= (4/x)+9
C.f(x)= 1/x g(x)= 4/x)+9
D.f(x)= 4/x^2 g(x)= 9

Answer 4

I consider case A:
\[\Large f\left( {g\left( x \right)} \right) = g\left( x \right) + 9 = ...\]
please substitute g(x9= 4/x^2, what do you get?

Answer 5

oops..g(x)=4/x^2, what do you get?

Answer 6

would it be f(x)= x+9

Answer 7

yes! it is, so we can write:
\[\Large f\left( {g\left( x \right)} \right) = g\left( x \right) + 9\]

Answer 8

ohh okay!

Answer 9

and how would i get a y value?

Answer 10

you have to replace g(x) with its definition 4/x^2

Answer 11

f(g(x))=g(x)+9 = f(g(x))=(4/x^2)+9

Answer 12

that's right!

Answer 13

thank you so much!

Answer 14

:)