Question

Find f(x) and g(x) so the function can be expressed as y = f(g(x)).
Y=8/(x^2)+4

Answer 1

There are many ways to do this.
For example: \[
\begin{array}{rcl}
g(x) &=& x \\
f(x) &=& \frac{8}{x^2+4} \\
f(g(x)) &=& \frac{8}{x^2+4}
\end{array}
\]

Answer 2

Then there is \[
\begin{array}{rcl}
g(x) &=& x^2 \\
f(x) &=& \frac{8}{x+4} \\
f(g(x)) &=& \frac{8}{x^2+4}
\end{array}
\]

Answer 3

Also \[
\begin{array}{rcl}
g(x) &=& x^2+4 \\
f(x) &=& \frac{8}{x} \\
f(g(x)) &=& \frac{8}{x^2+4}
\end{array}
\]

Answer 4

And finally: \[
\begin{array}{rcl}
g(x) &=& \frac{8}{x^2+4} \\
f(x) &=& x \\
f(g(x)) &=& \frac{8}{x^2+4}
\end{array}
\]

Answer 5

amazing thank you!!!:)

Answer 6

But do you understand it?

Answer 7

yes when you separate the x out of the equation and u join them to be f(g(x)) you are able to get the two away allowing for 8/(x+4) to be left out . am i right ?

Answer 8

giving you the f(x) and g(x)

Answer 9

you create two functions and plug one function into the other, and get the same function as a result.