Question

show the function f:R-R defined by f(x)=x^3 is bijection​

Answer 1

Answer:

differenciate it and you will get a quadratic function which is always positive for all value of x

so this function is an increasing function

hence one one

with no maximas and minimas because at x=0 for dy/dx and d2y/dx2 is zero hence it is an inflection point

and dy/dx is zero for jst a point not for a interval.

so you van check tht function is injective one one as you cant draw a horizontal line cutting graph at two points.

if it does it wouldn't be one one or bijection function

attaching two pics for ur clarity

first pic contains graph of function

(graph goes to infinity for x= infinity and -infinity for x= - infinity) and second pic show that even you go so closer to x=0 then also graph is not touching x axis this proves function is zero or there is tangent jst for a point or dy/dx is 0 jst for a point x=0 not for a interval