Question

If f(x) = `log_e{((1 - x))/((1 - x))}, |x| < 1, f{(2x)/((1 + x^2))}` is equal to ______.

Options

• 2f(x)

• (f(x))²

• 2f(x²)

• –2f(x)

Answer 1

If f(x) = `log_e{((1 - x))/((1 - x))}, |x| < 1, f{(2x)/((1 + x^2))}` is equal to 2f(x).

Explanation:

f(x) = log(1 – x) – log(1 + x)

`f((2x)/(1 + x^2)) = log(1 - (2x)/(1 + x^2)) - log(1 + (2x)/(1 + x^2))`

= `log  (1 - x)^2/(1 + x^2) - log  (1 + x)^2/(1 + x^2)`

= `log((1 - x)/(1 + x))^2`

= `2log  (1 - x)/(1 + x)`

= 2f(x)