how do you determine algebraically if an equation is one-to-one? For example: h(x)=4/(x^2)

Question

mathmate · Answer

If f(x1)=f(x2) where $x1\ne x2$ , then f(x) is not one to one.
Similarly, if f(x1) = y1 and f(x2)=y2, where x1=x2, then f(x) is not a function.

brittneygarcia5 · Answer

so, you plug in different numbers, and if two match up, then it is not a one-to-one function, right? @mathmate

mathmate · Answer

Yeah, but do not plug in numbers at random!  lol
Examine the function, and see if you can find distinct numbers x1 and x2 such that
f(x1)=f(x2).

brittneygarcia5 · Answer

so, how do you know which numbers to plug in?

brittneygarcia5 · Answer

@mathmate

mathmate · Answer

Hint:
Are you aware that $(-5)^2=(5)^2$

brittneygarcia5 · Answer

oh yeah duh, lol. so, look for patterns in the equation?

mathmate · Answer

Exactly.
Also, your post requests algebraic way of proving it one-to-one, but nothing stops you from using the horizontal line test as a check.

brittneygarcia5 · Answer

Thank you so much! @mathmate

mathmate · Answer

You're welcome!   :)