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## Algebra 1

### Course: Algebra 1>Unit 8

Lesson 13: Intro to inverse functions

# Finding inverse functions: linear

Sal finds the inverses of f(x)=-x+4 and g(x)=-2x-1. Created by Sal Khan.

## Want to join the conversation?

• really helpful this video but i would like to ask whether inverse functions are involved with or have anything to do with reciprocals? •   Not any relationship between reciprocal and inverse that I can think of. Unfortunately the notation for inverse is f⁻¹ which LOOKS like you're raising something to the -1st power which is taking the reciprocal. It's a coincidence: the symbols look the same but have nothing to do with each other.
• If the slope was -1/2 why didn't he go over 1 and down 2? •  Hi Andrew. Slope is rise/run, where rise is the amount of change in y-value (up or down), and run is the value of increase along the x-value (moving right). So -1/2 slope means down 1, right 2. I hope this helps you, but I'm tired and not sure this is written clearly.
• Why do we need to know the inverse of a function ? •  Inverses are all over, the inverse of + is - and the inverse of multiplication is division, and there are plenty of others! I can think of a few reasons for wanting to know. The first is kind of a reverse engineering thing. If you can find the inverse of a function then you can "undo" what the function did. For example, if you now the formula to convert degrees Celsius into degrees Fahrenheit, the inverse will convert Fahrenheit to Celsius. If a function does not have an inverse, it tells us something about the the function and it's shape. When we know if a function has an inverse or not, we can know that the function has certain properties and we can use those properties to understand more about the behavior of the function and its applications. You'll find out more about this if you move on to calculus or real analysis or number theory. So, like a lot about mathematics, you may not understand the "why" at the moment, but in time you will as your mathematical maturity grows.
Great Question! Have Fun!
• Hey, great video, i was just wondering if someone could help me understand what f'(x) meant, i was under the impression it was the inverse, but i know now that the inverse is f^-1(x) • Can you just switch the x's and y's before you solve in terms of y, that way you keep solving in terms of x, and you already find the f^-1(x) • Yes you can. That's actually how I've always done it myself. In the case of y = -x + 4 that's the only step you need in order to get the inverse. However, it still works the same way for y = x^2 + 4.

In that case you can find the inverse of the function y = x^2 + 4 with the following steps:
x = y^2 + 4
x - 4 = y^2
x = ±sqr(y - 4) sqr = square root sign.

And it works for Sal's second example.
y = -2x -1
x = -2y -1 (switch variables)
x + 1 = -2y
-x -1 = 2y
y = -x/2 -1/2
• Why do you swap the y for the x? I would rather understand why than memorize. • whats the difference between inverse function and reciprocal functions ? • I think giving an example is the easiest way to explain this.
Given a function f(x)=5x+3
Find its reciprocal and its inverse.
answer 1: `reciprocal of f(x)=1/f(x) = 1/(5x+3)`
answer 2: `inverse of f(x)=(x-3)/5`
solution for number 2:
`1st step` solve for f(x)
f(x)=5x+3 original function
f(x)-3=5x+3-3 subtracting fro both sides
f(x)-3=5x we get this then
(f(x)-3)/5=x dividing both sides by 5
`2nd step` swap the sides and let f(x)=x and x=inverse of f(x) or just f(x)
inverse of f(x)=(x-3)/5   