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### Course: Algebra (all content) > Unit 7

Lesson 2: Inputs and outputs of a function- Worked example: matching an input to a function's output (equation)
- Function inputs & outputs: equation
- Worked example: matching an input to a function's output (graph)
- Worked example: two inputs with the same output (graph)
- Function inputs & outputs: graph

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# 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?(13 votes)
- 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.(54 votes)

- so whenever it says f(x) is equal to something, they actually meant the y value?(14 votes)
- 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.(18 votes)

- How would I type a more complex input on the calculator to find a corresponding output? What are the steps?(14 votes)
- I'm confused i mean i get it but yet i dont get it? any advise?(6 votes)
- Ask Questions. The members of khan academy are here to help you.(4 votes)

- alright , so how do you know if the answer is a positive , or negative answer ?(4 votes)
- 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 !(4 votes)

- 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!(5 votes)
- where do the negative 2's come from(3 votes)
- The opposite of multiply by negative 2 is to divide by negative 2.(5 votes)

- where did the 13 come from(4 votes)
- The 13 was given to you as part of the problem statement. It wasn't calculated in the problem.(2 votes)

- 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(2 votes)
- 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.(5 votes)

- g(t)=−9t−4

g( )=23

Find all the inputs that correspond to a given function output, using the function's formula.(3 votes)- We want to find all possible values of 𝑡, for which 𝑔(𝑡) = 23

In other words, we want to solve the equation

−9𝑡 − 4 = 23(3 votes)

## Video transcript

The function f is defined as follows: f of t is equal to negative
two t plus five. So whatever we input into this function, we multiply it times negative two,
and then we add five. So what is the input value
for which f of t is equal to 13? So if f of t is equal to 13, that
means that this thing over here is equal to 13 for some t, for some input. So we can just solve the equation,
negative two t plus five is equal to 13. So let's do that. Negative two t plus five is equal to 13. Well, we can subtract
five from both sides. I'm just trying to isolate the t
on the left hand-side. So, subtract negative five from the left, that's the whole reason why we
did that, so those disappear. But we have to do it
from the right as well. So you have 13 minus five is eight. And on the left hand-side
you still have your negative two t. So you have negative two t
is equal to eight. Now to just have a t on
the left hand-side, I want to divide both sides
by negative two. And I'm left with, t is equal to
eight divided by negative two, is equal to negative four. So you input negative four
into this function and it will output 13. Or we could write that f of
negative four is equal to 13. But this, is what they are looking for. This is the input value. Negative four is the input value
for which f of t is equal to 13. f of negative four is equal to 13.