Question

If f(x) = x^x ; [a, ¥) ® [b, ¥) is an invertible function then the

minimum values of a & b are –

• A. $\frac{1}{e},e^{- 1/e}$
• B. e, e^1/e
• C. $\frac{1}{e},e^{- e}$
• D. None of these

Answer 1

Answer: (A)

$\frac{1}{e},e^{- 1/e}$

Answer 2

f(x) = x^x

f '(x) = x^x (1 + lnx) = 0 ̃ x = $\frac{1}{e}$

\ a = $\frac{1}{e}$ & b = e^–1/e