Question

f(x)=log(1+x/1-x)then f(x¹)+f(x²)=?

Answer 1

Answer :

Given that,

f (x) = log {(1 + x)/(1 - x)}

⇒ f (x¹) = log {(1 + x)/(1 - x)}

Then, f (x²)

= log {(1 + x²)/(1 - x²)}

Now,

f (x¹) + f (x²)

= log {(1 + x)/(1 - x)} + log {(1 + x²)/(1 - x²)}

= log [{(1 + x)(1 + x²)}/{(1 - x)(1 - x²)}]

= log [{(1 + x)(1 + x²)}/{(1 - x)(1 + x)(1 - x)}]

= log [(1 + x²)/{(1 - x)(1 - x)}]

= log [(1 + x²)/(1 - x)²]

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