# Injective and surjective

• Mar 12th 2008, 06:44 PM
tironci
Injective and surjective
Hi everyone,

I have a math problem i am having a hard time solving. Can someone please help me?

Show whether or not the function f:R+ -> R+ defined by f(x) = (1/x^2) is

Injective (one-to-one) or
Surjective(onto)

• Mar 12th 2008, 06:49 PM
ThePerfectHacker
Quote:

Originally Posted by tironci
Hi everyone,

I have a math problem i am having a hard time solving. Can someone please help me?

Show whether or not the function f:R+ -> R+ defined by f(x) = (1/x^2) is

Injective (one-to-one) or
Surjective(onto)

Say $\displaystyle f(x) = f(y) \implies \frac{1}{x^2} = \frac{1}{y^2} \implies x^2 = y^2 \implies x = y \mbox{ since }x,y>0$.

For any $\displaystyle y\in \mathbb{R}^+$ let $\displaystyle x=1/\sqrt{y}$ then $\displaystyle x\in \mathbb{R}^+$ and $\displaystyle f(x) = y$.
• Mar 13th 2008, 07:21 PM
tironci
Injective and surjective
So, it is one-to-one and onto?

Thank you
• Mar 13th 2008, 07:35 PM
ThePerfectHacker
Quote:

Originally Posted by tironci
So, it is one-to-one and onto?

What is the definition of one-to-one? What is the definition of onto? Does the above post prove those things?