The function f defined by fx x is onto because for any real

The function f: defined by f(x) = x³ is onto because for any real number , we have that is a real number and . Consider the same function defined on the integers g: by g(n) = n³. Explain why g is not onto and give one integer that g cannot output.

Solution

G is not onto for g:

we know that for onto .. the relation must have all values of it\'s codomain values

because we will not get all integer values as codomain

For example :

At n=1:

g(1)=1^3=1

at n=2

g(2)=2^3 =8

but not values of \'n\' can given g(n) as 2, 3, 4, 5, 6, 7,

While these values are also part of integer zet or Z

Hence , for onto , we should get these values of g(n) as well

but we won\'t get these values

that\'s why g is not onto on Z..............Answer