Andrew M. answered • 04/06/16

Tutor

New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

http://www.mathsisfun.com/sets/injective-surjective-bijective.html

The above link has great information on the meaning of

injective, surjective and bijective function... Bijective functions are

both injective and surjective and basically means there is a perfect "one-to-one

correspondence" between the members of the sets.

Every input value x for function f(x) has one and only one output value f(x)...

Every output value of f(x) has one and only one corresponding input value x.

**f(x) = x**

^{3 }**is a bijective cubic function.**

For any input value x there is one and only one output value for f(x).

For any output value of f(x) there is only one input value x that results

in that output value.

**f(x) = 2x**

^{3}- 3x^{2}- 3x +2**is NOT a bijective cubic function**because more than one input

value "x" can produce the same output value for f(x)

f(-1) = 2(-1) - 3(1) -3(-1) + 2 = -5 + 5 = 0

f(2) = 2(8) - 3(4) - 3(2) + 2 = 16-12-6+2 = 0

Since two different input values x create the same

output value for f(x) this is not a bijective function.

John G.

^{3}is still bijective. It's just x^{3}reflected over the x-axis.^{3}= -1, not 104/06/16