Given f(x) = x^3 and g(x) = 2x + 1 where f,g: Q-Q, show that gof is a bijection.

I plug in f into g, and idk what to do from there. Do I need to show that it's 1-1 and onto?

Question

Given f(x) = x^3 and g(x) = 2x + 1 where f,g: Q->Q, show that gof is a bijection. 

I plug in f into g, and idk what to do from there. Do I need to show that it's 1-1 and onto?

rock_mit182 · Answer

|dw:1395636721221:dw|

rock_mit182 · Answer

is this linear algebra ?

anonymous · Answer

Discrete math

amistre64 · Answer

since f and g both have inverses, they are 1 to 1

since they are both odd degrees, they have the same domain/range as well, so onto.

not sure how rigorous that is tho

amistre64 · Answer

hmm, show that g(f) is also 1-1 and onto ....

g(f) = 2x^3 + 1  is just a modified f ...

amistre64 · Answer

2(a/b)^3 + 1 = 2(m/n)^3 + 1

2(a/b)^3 = 2(m/n)^3

(a/b)^3 = (m/n)^3

now we are left to showing that f is 1-1 and onto .... maybe