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# What's an inverse?

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I need help on Algebra 2

Sep 5, 2017

#1
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Sep 5, 2017
#2
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If you're referring to an inverse function.....the original function pairs some x with some y

The inverse reverses these coordinates

Example

Original function       f(x)  =   3x + 5

Inverse function      f-1(x) = [ x - 5] / 3

Note that  if  (0, 5)   is a point on the original function.......then  note that ( 5, 0)  is on the inverse function   Sep 5, 2017
edited by CPhill  Sep 5, 2017
#3
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It's also possible that this user is referring to either the additive or multiplicative inverse.

The additive inverse is fancy terminology for the opposite. In algabraic terms, $$a\Rightarrow-a$$. Here are some examples

1) $$5\Rightarrow-5$$

2) $$0\Rightarrow0$$

3) $$\frac{3}{5}\Rightarrow-\frac{3}{5}$$

4) $$\pi\Rightarrow-\pi$$

These examples are simple ones. But what if you need to find the inverse of $$\frac{\frac{1}{2}a}{\frac{3}{4}a}$$? Well, a tip I can give you is that if you take the sum of the number and its additive inverse, you will always get 0. Therefore, we can find the additive inverse by setting up the equation $$\frac{\frac{1}{2}a}{\frac{3}{4}a}+x=0$$. Once we solve for x, we will have the additive inverse.

The mutliplicative inverse affects the number in the following fashing: $$a\Rightarrow\frac{1}{a}$$. This is also known as the reciprocal. Just like before, for a complicated example, know that when a number and multiplicative inverse are multiplied, it will always yield 1.

Sep 5, 2017