Question

Let g be the inverse of the continuous function f, Let there be a point (α, β), 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

Answer 1

Correct option (B)(C)

Explanation:

As the point (α , β), **** 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.