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  4. If f(x) = (x-1/x+1), then f (2x) is equal to

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Q. If $f\left(x\right) = \frac{x-1}{x+1},$ then $f (2x)$ is equal to

Relations and Functions

Solution:

Given $f\left(x\right) = \frac{x-1}{x+1}$
$\therefore \quad f\left(2x\right) = \frac{2x-1}{2x+1}$
$=\frac{2\left(2x-1\right)}{2\left(2x+1\right)}$ (multiply and divide by 2)
$= \frac{4x-2}{4x+2} = \frac{3x+x-3+1}{3x+x+3-1} = \frac{3\left(x-1\right)+x+1}{3\left(x+1\right)+x-1}$
$= \frac{3\left[\frac{x-1}{x+1}\right]+1}{\frac{x-1}{x+1}+3} = \frac{3f\left(x\right)+1}{f\left(x\right)+3}$