Question

Given f(x) = `log((1 + x)/(1 - x))` and g(x) = `(3x + x^3)/(1 + 3x^2)`, then fog(x) equals

Options

• – f(x)

• 3f(x)

• [f(x)]³

• None of these

Answer 1

3f(x)

Explanation:

Since, g(x) = `(3x + x^3)/(1 + 3x^2)`, (say)  ......(i)

∴ f[g(x)] = f(y) = `log((1 + y)/(1 - y))` 

= `log {(1 + (3x + x^3)/(1 + 3x^2))/(1 - (3x + x^3)/(1 + 3x^2))}`

⇒ f(g(x)) = `log((1 + x)/(1 - x))^3 = 3log((1 + x)/(1 - x))` = 3f(x)