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Question

If f:R - {±1} R is defined by f(x)=log1+x1x, then show that f(2x1+x2)=2f(x)

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Solution

f(x)=log1+x1x
f(2x)=log1+2x12x
2f(x)=2log1+x1x
=log(1+x1x)2
=log1+x2+2x1+x22x...(1)
f(2x1+x2)=log∣ ∣ ∣ ∣1+2x1+x212x1+x2∣ ∣ ∣ ∣
=log1+x2+2x1+x22x...(2)
from (i) & (ii)
f(2x1+x2)=2f(x)

1146991_876761_ans_83766efaba1248adabcb31f7ca8d9d46.jpg

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