If f ( x ) = x - 1 x + 1 , then f ( 2 x ) is

Question

If $f (x)$ $= \frac{x - 1}{x + 1}$ , then $f (2 x)$ is

Smart Achievers · Accepted Answer

(2)

$f (x)$ $= \frac{x - 1}{x + 1} \Rightarrow x = \frac{f (x) + 1}{1 - f (x)}$

$Now,$ $f (2 x)$ $= \frac{2 x - 1}{2 x + 1} = \frac{2 [\frac{f (x) + 1}{1 - f (x)}] - 1}{2 [\frac{f (x) + 1}{1 - f (x)}] + 1} = \frac{3 f (x) + 1}{f (x) + 3}$

Solution

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

1 $\frac{f (x) + 1}{f (x) + 3}$

2 $\frac{3 f (x) + 1}{f (x) + 3}$

3 $\frac{f (x) + 3}{f (x) + 1}$

4 $\frac{f (x) + 3}{3 f (x) + 1}$

Ans.
(2)

$f (x)$ $= \frac{x - 1}{x + 1} \Rightarrow x = \frac{f (x) + 1}{1 - f (x)}$

$Now,$ $f (2 x)$ $= \frac{2 x - 1}{2 x + 1} = \frac{2 [\frac{f (x) + 1}{1 - f (x)}] - 1}{2 [\frac{f (x) + 1}{1 - f (x)}] + 1} = \frac{3 f (x) + 1}{f (x) + 3}$

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Solution

Q. If f(x)=x-1x+1, then f(2x) is

1 f(x)+1f(x)+3

2 3f(x)+1f(x)+3

3 f(x)+3f(x)+1

4 f(x)+33f(x)+1

Ans. (2) f(x)=x-1x+1⇒x=f(x)+11-f(x) Now, f(2x)=2x-12x+1=2[f(x)+11-f(x)]-12[f(x)+11-f(x)]+1=3f(x)+1f(x)+3