Injective and surjective

**tironci** · March 12th 2008, 06:44 PM

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)

Thank you in advance

**ThePerfectHacker** · March 12th 2008, 06:49 PM

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)

Thank you in advance

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

For any $y\in \mathbb{R}^+$ let $x=1/\sqrt{y}$ then $x\in \mathbb{R}^+$ and $f(x) = y$ .

**tironci** · March 13th 2008, 07:21 PM

So, it is one-to-one and onto?

Thank you

**ThePerfectHacker** · March 13th 2008, 07:35 PM

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?

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