If f(x) = (x - 1) / (x + 1), then find the value of f(2x).

Solution:

Given , f(x) = (x - 1) / (x + 1).

Change the subject of formula from f(x) to that for x.

If f(x) = (x - 1) / (x + 1),then, the value of f(2x) is equal to (3f(x) + 1) / (f(x) + 3).

Given below is the detailed solution using a simple operation, known as componendo and dividendo.

Applying componendo and dividendo on numerator and denominator, we get,

[f(x) + 1] / [f(x) - 1] = 2x/-2

[f(x) + 1] / [f(x) - 1] = -x

==> [f(x) + 1] / [1 - f(x)] = x

Now replacing x by 2x in the initial equation, and using the value of x in terms of f(x), we get,

f(2x) = (2x - 1) / (2x + 1)

=  {2[f(x) + 1 / 1 - f(x) ] - 1} / { 2[f(x) + 1 / 1 -  f(x)] + 1}

= [2f(x) + 2 -1 + f(x)] / [2f(x) + 2 + 1 - f(x)]

= (3 f(x) + 1) / (f(x) + 3)

Thus, If f(x) = (x - 1) / (x + 1),then, the value of f(2x) is equal to (3f(x) + 1) / (f(x) + 3)

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If f(x) = (x - 1) / (x + 1), then find the value of f(2x).

Summary:

If f(x) = (x - 1) / (x + 1),then, the value of f(2x) is equal to (3f(x) + 1) / (f(x) + 3).