Jika f (x) = x-1/x+1 maka tentukan nilai f (2x).
(x) = ( x – 1 ) / ( x + 1 ) ………… (1)
( x + 1 ). (x) = x – 1
- (x) + (x) = x – 1
- (x) – x = – 1 – (x)
- [ (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) ]
10