SOLUTION: Prove or disprove that h(x)=2x^3+1, where in h: integers (Z) → integers (Z) is a bijective function.

Question 1167228: Prove or disprove that h(x)=2x^3+1, where in h: integers (Z) → integers (Z) is a bijective function.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

The map   x ---> 2x^3+1   from integer numbers to integer numbers is injective, but is not bijective.

In other words, the image of this map does not cover the entire set of integer numbers.

For example, the number 11 does not belong to the image, since the equation

            2x^3 + 1 = 11

has no solution in integer numbers (due to obvious reasons).

RELATED QUESTIONS
given set Z(26) = {0,1,2,3,...25} Let a and b be integers. Consider the function f:... (answered by ikleyn)

Define g: R---> Z by the rule g(x)=9x+5, Vx E R Is g(x) bijective... (answered by jim_thompson5910)

Construct two examples of bijective function from ZxZ to Q where Z is set of all integers (answered by CPhill,ikleyn)

Prove that the function is bijective. The function is f: N--->Z f(x)=(1+(−1)^x *... (answered by richard1234)

Use proof by contradiction to prove/disprove that no integers x and y exist such that... (answered by ikleyn)

Find a linear function h given h(−1) =−6 and h(−4)=−8. The linear... (answered by josgarithmetic)

2^x 3^y 5^z=2000 where x,y,z are integers. Find the value of... (answered by ikleyn)

Hello, please help me with my homework: In an equilateral triangle, take a point inside... (answered by richard1234)

RATE OF CHANGE PROBLEMS A function is given. Determine the average rate of change of... (answered by ewatrrr)