Determine the domain codomain and range Also decide if the f

Determine the domain, codomain, and range. Also, decide if the function is injective/surjective/bijective.

f : R R given by f(x) = x 3 + 2.

Solution

For Injective:

Start with f(a)=f(b)

ie 3a+2=3b+2

ie 3a=3b

ie a=b

hence the fn is injective or one to one.

For Bijective:

Ley y=3x+2

ie 3x=y-2

x=(y-2)/3

So for all y belonging to R, we have a corresponding value of x in R. Hence range and codomain are same. So the function is bijective.