Mark the correct alternative in the following:

Question:

Mark the correct alternative in the following:

Every invertible function is

A. monotonic function

B. constant function

C. identity function

D. not necessarily monotonic function

Solution:

Formula:- (i) The necessary and sufficient condition for differentiable function defined on (a,b) to be strictly increasing on $(a, b)$ is that $f^{\prime}(x)>0$ for all $x \in(a, b)$

If $f(x)$ is strictly increasing function on interval $[a, b]$, then $f^{-1}$ exist and it is also a strictly increasing function

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