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asked ago in Mathematics by (53.5k points)

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

(A) the equation f(x) = g(x) has infinitely many solutions 

(B) the equation f(x) = g(x) has at least 3 solutions

(C) f must be a decreasing function of x

(D) g can be an increasing function of x

1 Answer

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answered ago by (21.1k points)
selected ago by
 
Best answer

Correct option  (B)(C)

Explanation:

As the point (α , β), lies on both f(x) and g(x) , the point (β,α) 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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