Question

How would i find the range without a calculator or graph for (4x)/((x^2)+2)?
I know what it is but i have to show the work and i dont know how to algebraically

Answer 1

\[\frac{4x}{x^2+2}=y\] without using calc you can find the range by solving for \(x\)

Answer 2

what would i do after this?
i got 4x=yx^2+2y then -2y=yx^2-4x
how would i solve for x with more than one x?

Answer 3

\[ 4x=yx^2+2y\]
\[yx^2-4x-2y=0\] use \(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)with
\[a=y,b=-4,c=-2y\] and basically you have to make sure that \(b^2-4ac\geq 0\) otherwise it is notdefined

Answer 4

\[16-4\times y\times (-2y)\geq 0\]
\[16+8y^2\geq 0\] etc

Answer 5

i made some mistake

Answer 6

\[yx^2-4x+2y=0\]
\[16-8y^2\geq 0\] etc

Answer 7

\[2-y^2\geq0\]
\[-\sqrt{2}\leq y\leq \sqrt{2}\]

Answer 8

THANK YOU