Question 8

$$f(x) = \frac{2x + 2}{2x - 2}$$, where y = f(x). Find the ratio of x to f(y).

Solution

$$f\left(y\right)=f\left(f\left(x\right)\right)$$

or, $$f\left(y\right)=f\left(\frac{2x+2}{2x-2}\right)$$

$$f\left(y\right)=\frac{2\left(\frac{2x+2}{2x-2}\right)+2}{2\left(\frac{2x+2}{2x-2}\right)-2}$$

or, $$f\left(y\right)=\frac{8x}{8}=x$$

Therefore x:f(y) = 1:1

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