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### Course: Class 11 Physics (India)>Unit 3

Lesson 9: Inputs and outputs of a function

# Worked example: matching an input to a function's output (equation)

Sal finds the input value for which f(t)=13, given that f(t)=-2t+5.

## Want to join the conversation?

• where did you get the -5's from?
• Try to imagine that you are 'removing' the 5's from both sides in order to isolate t (Which was what we are trying to find). In the equation -2t+5=13, we know that whatever -2t is, by adding 5 we get 13, so we have to subtract 5 in order to see what -2t is on its own.

In a more basic example you could say that x+2=10, by subtracting 2 from both sides we get x=8, because on the left we get x+2-2 which is simply x, and on the right 10-2 is 8. which makes sense, because 8+2=10. I hope this helps.
• so whenever it says f(x) is equal to something, they actually meant the y value?
• Yes, because the y axis is where you plot the output. Saying "f(x)" instead of "y" highlights the fact that you put a value for x into the function and get out a value for y. The function describes how y varies with x.
• I'm confused i mean i get it but yet i dont get it? any advise?
• How would I type a more complex input on the calculator to find a corresponding output? What are the steps?
• Man, I'm a software dev working on AI frameworks, and realized I didn't know enough calculus to really fix some of the optimizations and gradients. I tried learning calculus on khan academy, but then I realized I didn't know Algebra as in-depth or as "creatively" as I thought I did. So here I am, binging Algebra videos. I'm half worried I'll have to go back to learning ABCs, HA!
• alright , so how do you know if the answer is a positive , or negative answer ?
• If the answer is a positive, it just a number by itself.
E.g = 3,2,1023,42,1 are all positive numbers.

If the answer in negative, then it has a "-" preceding a number.
E.g -2,-35,-13,-34, are all negative numbers.
Also remember this:
- Positive/positive = positive
- Negative/negative = positive
- Negative/positive = negative
- Positive/negative = negative

hope that helps !
• where do the negative 2's come from
• The opposite of multiply by negative 2 is to divide by negative 2.
• where did the 13 come from
• The 13 was given to you as part of the problem statement. It wasn't calculated in the problem.
• For the first term, sal subtract 13-5= 8 then for the second time sal divide 8 by -2 =-4 instead of subtracting again that will be 6, I wanna understand why he divided
• Sal is finding the input value for the function f(t) = -2t+5 when the output equals 13.
As Sal shows, you basically need to solve: -2t+5 = 13
Remember, we move items across the "=" by using opposite operations. To solve that equation and isolate "t", you would need to:
1) Ssubtract 5 (subtraction is the opposite of +5)
2) Divide by -2 (because division is the opposite of multiplication).
Hope this helps.