Jika f (x) = x-1/x+1 maka tentukan nilai f (2x).

Jika f (x) = x-1/x+1 maka tentukan nilai f (2x).

(x) = ( x – 1 ) / ( x + 1 ) ………… (1)

( x + 1 ). (x) = x – 1

  1. (x) + (x) = x – 1
  2. (x) – x = – 1 – (x)
  3. [ (x) – 1 ] = – [ 1 + (x) ]

x = [ 1 + (x) ] / [ 1 – (x) ] ……………… (2)

dari (1),

(2x) = [ (2x) – 1 ] / [ (2x) + 1 ]

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

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

= { 2 + 2.ƒ(x) – 1 + (x) } / { 2 + 2.ƒ(x) + 1 – (x) }

= [ 1 + 3.ƒ(x) ] / [ 3 + (x) ]

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