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

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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.