Most Important Selected Qs for JEE AdvancedMathematicsContinuity and Differentiability

Let g be the inverse of the continuous function f , Let there be a point ( , ) , where , is such that it satisfies each of y=f(x) and y=g(x) then

Options

Athe equation f(x)=g(x) has infinitely many solutions
Bthe equation f(x)=g(x) has atleast 3 solutions
Cf must be a decreasing function of x
Dg can be an increasing function of x

Correct answer

C. f must be a decreasing function of x

Step-by-step solution

As the point ( , ) , lies on both f(x) and g(x) , the point ( , ) will also lie on both the curves and as the functions are continuous they must cross (meet on) the line y=x in between. f must be on decreasing path, for all these to happen.

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