Determine algebraically whether f(x)=(2x+1)/(x-4) is one-to-one.

Determine algebraically whether $f\left(x\right)=\frac{2x+1}{x-4}$ is one-to-one.
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moderrockblog09
Solution:
Given $f\left(x\right)=\frac{2x+1}{x-4}$
To show that f is 1-1, you could show that
$f\left(x\right)=f\left(y\right)⇒x=y\phantom{\rule{0ex}{0ex}}\frac{2x+1}{x-4}=\frac{2y+1}{y-4}\phantom{\rule{0ex}{0ex}}\left(2x+1\right)\left(y-4\right)=\left(2y+1\right)\left(x-4\right)\phantom{\rule{0ex}{0ex}}2xy-8x+y-4=2xy-8y+x-4\phantom{\rule{0ex}{0ex}}-8x-x=-8y-y\phantom{\rule{0ex}{0ex}}x=y$
So f(x) is one-to-one