Finding and interpreting inverse functions
About this video
The cost of a robotics team's 3D-printed parts is C = 7p + 25. The video finds the inverse by solving for p, giving p = (C - 25)/7. It explains that the inverse takes a total cost as input and gives the number of parts ordered as output.
You'll be able to
- find the inverse of a linear function by solving for the input variable.
- explain what the input and output of an inverse function mean in context.
- rule out wrong interpretations of an inverse function.
Key words
- inverse function
- A function that goes the other way: it takes the original output as input and gives back the original input.
- input
- The value you put into a function.
- output
- The value a function gives back.
Transcript
- [Instructor] We're told a robotics team orders 3D printed parts for a competition build. The equation C = 7p + 25 represents the total cost, C as a function of the number of parts ordered, p. Write an equation, I guess this has two parts. First they say write an equation that represents the inverse of the given function.
And then the second part, explain what the inverse of this function means. And let me scroll down a little bit so we can get that last choice in there. So pause this video, have a go at this before we do this together. Alright, so let's do the first part where we wanna write an equation that represents the inverse.
So right now this function, if you were to give it a number of parts, it is going to then by looking at this function definition, it's going to give you the cost. The inverse wants to go the other way. If you are given the cost, then it will output the number of parts that you would order to get that cost.
So if our original function is C = 7p + 25, what we really just want to do is algebraically manipulate this so that we solve for p. As I said, right now you input a p, it gives you a C. We want to input a C to get a p. Alright, so to isolate the p on one side, I can subtract 25 from both sides.
So I get C - 25 = 7p and now I can divide both sides by seven. So I just have a p on the right hand side and I get C - 25/7 = p, which is of course the same thing as p = C - 25/7. Either of these is fine and what you can see here is now if you give me a C, I can evaluate this expression to get a p.
Input a C output a p. Up here input a p output a C. Alright, so explain what the inverse of this function means. It gives how many parts were ordered based on the total cost. That's looking pretty good. If you were to give the total cost, it gives how many parts were ordered.
If you input this, it outputs that. I like this choice, but let's look at the other ones. It gives a number of parts the team can order to remain on budget. This one, you might associate cost with budget, but we don't have an notion of what the cost has to be or that the cost has to be below a certain amount.
So we don't really know anything about the budget. So I would rule that one out. It gives the total cost before any per-part charges were applied. No, it definitely does not give the total cost. This inverse gives a number of parts based on a cost. It gives the cost of ordering one part.
No, the function output gives parts not cost. So yes, I like choice A.
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