Question

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

y = Two divided by x squared. + 3

Answer 1

Is the written equation A or B:

\(A.\phantom{.}y=\frac{2}{x^2}+3\)
\(B.\phantom{.}y=\left(\frac{2}{x}\right)^2+3\)

Answer 2

It makes a difference!

Answer 3

It is equation A

Answer 4

Oh okay! Well basically, What your doing is cutting out a piece of equation A (like the "\(x\)" or "\(x^2\)" or "\(\frac{2}{x^2}\)" or even "\(\frac{2}{x^2}+3\)" And saying that's going to be \(g(x)\), and \(f(x)\) would be what the function would look like if it didn't have that part! So for example watch this:

Lets say \(g(x)=\frac{2}{x^2}\): Then \(f(x)=x+3\) Because that's the only way that \(f\left(g(x)\right)=\frac{2}{x^2}+3\) Makes sense?

I could alse very similarly say that \(g(x)=x^2\) and that \(f(x)=\frac{2}{x}+3\) Because when I put the "\(x^2\)" from \(g(x)\) into the "\(x\)" from \(f(x)\) then ill get \(\frac{2}{x^2}+3\). Makes sense?

Answer 5

This makes sense now, thanks!

Answer 6

Anytime goldcard :-)

Answer 7

First of all @goldcard : A Warm Welcome to 'Open Study'. Please Read CoC (compulsory to read by all "Open Study" users) : http://openstudy.com/code-of-conduct