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Question: If f(x) = \(f^{- 1}( - 3)\), then...

If f(x) = f−1(−3)f^{- 1}( - 3), then

A

f(x) is differentiable at x = 0

B

f(x) is continuous at x = 0

C

f(x) is differentiable at x = 1

D

None of these

Answer

f(x) is continuous at x = 0

Explanation

Solution

f(x) = {ex;x≤0∣x−1∣x>0\left\{ \begin{array} { c l } \mathrm { e } ^ { \mathrm { x } } ; & \mathrm { x } \leq 0 \\ | \mathrm { x } - 1 | & \mathrm { x } > 0 \end{array} \right.

continuous at x = 0