injective function and image

[LeroyTsruya]

Hi all!
i have a problem solving this:
given the function g: R->R
g(x) = (2x^2 - x)/(3x^2 +x + 1)

I have to determine g is an injective function,
and also find its image.

any ideas?

Thanks!

[MAS1]

Originally Posted by LeroyTsruya

Hi all!
i have a problem solving this:
given the function g: R->R
g(x) = (2x^2 - x)/(3x^2 +x + 1)

I have to determine g is an injective function,
and also find its image.

any ideas?

Thanks!

The function g is injective if for all a and b in A, if g(a) = g(b), then a = b; that is, g(a) = g(b) implies a = b. Equivalently, if a ≠ b, then g(a) ≠ g(b).

Therefore, since g(0) = (2(0)^2 - 0)/(3(0)^2 + 0 + 1) = (0)/(1) = 0 and
g(1/2) = (2(1/2)^2 - (1/2))/(3(1/2)^2 + (1/2) + 1) = (0)/(2 1/4) = 0

then the function g(x) is not injective.

I'm not sure what you mean by image. Could you define it ?

[jmw106462]

What Mas1 said.