Query

[Neha Gupta]

Guys, should it be a or c?

[Asd1995]

(a), because inverse of a function is basically its mirror image in the line y=x. So only way mirror images coincide is if they are at 0 distance from the mirror i.e they lie on y=x

[Neha Gupta]

yes, exactly, i am also getting this only, but see:



This answer is given.. not getting that..

[Econ17]

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[Asd1995]

My bad, they may not necessarily intersect there. Counter example would be f(x)=-x^3 and g(x)=-(x)^1/3, which intersect at (-1,1) and (1,-1) so (c) is correct. For the points to lie on y=x the function has to be strictly increasing.

[Econ17]

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[Asd1995]

The question is IF, they intersect, they'd do it on y=x. This is not necessarily correct though.

[Econ17]

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[Neha Gupta]

Ok thanks:)

[Gin_no]

Correct answer is (A) ?

[Neha Gupta]

its C

[Gin_no]

According to your solution they are not intersection point, P(α, β) and Q(β,α) intersect only if they are same point's coordinate because they are intersection point of f and inv f. So α = β and slope of a single point is undefined.

If P(a,b) and Q(c,d) are two different intersection point of f and inv f then should lie on y = x. and
slope of PQ will be 1.

Do lnx and e^x intersect each-other? how and where ?