Question

The inverse of f(x) = `2/3 (10^x - 10^-x)/(10^x + 10^-x)` is ______.

पर्याय

• `1/3 log_10  (1 + x)/(1 - x)`

• `1/2 log_10  (2 + 3x)/(2 - 3x)`

• `1/3 log_10  (2 + 3x)/(2 - 3x)`

• `1/6 log_10  (2 - 3x)/(2 + 3x)`

Answer 1

The inverse of f(x) = `2/3 (10^x - 10^-x)/(10^x + 10^-x)` is `underlinebb(1/2 log_10  (2 + 3x)/(2 - 3x))`.

Explanation:

If y = `2/3 (10^x - 10^-x)/(10^x + 10^-x)`,

10^2x = `(3y + 2)/(2 - 3y)`

or x = `1/2 log_10  (2 + 3y)/(2 - 3y)`

∴ f^–1 (x) = `1/2 log_10  (2 + 3x)/(2 - 3x)`.