$f (x) = \frac{x + 1}{2 x - 1} \Rightarrow f (2 x) = ?$ $f(x)= (x+1)/(2x-1) =>f(2x)= ?$ result $f (2 x) = \frac{4 f (x) + 1}{2 f (x) + 5}$ $f(2x)=(4f(x)+1)/(2f(x)+5)$ but how find it ?

Question

$f (x) = \frac{x + 1}{2 x - 1} \Rightarrow f (2 x) = ?$ $f(x)= (x+1)/(2x-1) =>f(2x)= ?$

$f (2 x) = \frac{4 f (x) + 1}{2 f (x) + 5}$ $f(2x)=(4f(x)+1)/(2f(x)+5)$
but how find it ?

1393 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-07T11:42:43

$f (x) = \frac{x + 1}{2 x - 1}$ $f(x)=(x+1)/(2x-1)$ .

To find, $f (2 x)$ $f(2x)$ , let, $2 x = t$ $2x=t$ . Then,

$Reqd. Value= f (2 x) = f (t)$ $"Reqd. Value="f(2x)=f(t)$ ,

$= \frac{t + 1}{2 t - 1}$ $=(t+1)/(2t-1)$ ,

$=(2x+1)/{2(2x)-1}............[because, t=2x]$ .

$rArr "Reqd. Value="f(2x)=(2x+1)/(4x-1)............(star)$ .

Next, $f(x)=(x+1)/(2x-1)$ ,

$rArr 4f(x)+1=4{(x+1)/(2x-1)}+1$ ,

$={(4x+4)+(2x-1)}/(4x-1)$ ,

$:. 4f(x)+1=(6x+3)/(2x-1).............(star1)$ .

Also, $2f(x)+5=2{(x+1)/(2x-1)}+5$ ,

$={(2x+2)+5(2x-1)}/(2x-1)$ ,

$rArr 2f(x)+5=(12x-3)/(2x-1).............(star2)$ .

$"Therefore, "(star1) and (star2) rArr (4f(x)+1)/(2f(x)+5)$ ,

$=(6x+3)/(12x-3)={3(2x+1)}/{3(4x-1)}$ .

$:. f(2x)=(2x+1)/(4x-1)=(4f(x)+1)/(2f(x)+5)$ .