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

Solution:

A function gives a relationship between an input and output variable where the output is dependent upon the input.

Let's look into the steps below

ƒ(x) = ( x - 1 ) / ( x + 1 ) 

By cross multiplication,

⇒ ( x + 1 ). ƒ(x) = x - 1

⇒ x ƒ(x) + ƒ(x) = x - 1

⇒ x ƒ(x) - x = - 1 - ƒ(x)

⇒ x [ ƒ(x) - 1 ] = - [ 1 + ƒ(x) ]

⇒ x = [ 1 + ƒ(x) ] / [ 1 - ƒ(x) ] ----------------- (1)

Now, let's evaluate ƒ(2x)

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

Substituting the value of x from (1) in (2) we get,

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

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

= { 2 + 2 ƒ(x) - 1 + ƒ(x) } / { 2 + 2 ƒ(x) + 1 - ƒ(x) }

= [ 1 + 3 ƒ(x) ] / [ 3 + ƒ(x) ]

Thus, the value of f (2x) is [ 1 + 3 ƒ(x) ] / [ 3 + ƒ(x) ]

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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 [ 1 + 3 ƒ(x) ] / [ 3 + ƒ(x) ]