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

CCSS.Math:

## Video transcript

the function f is defined as follows f of T is equal to negative 2t plus 5 so whatever we input into this function we multiply it times negative 2 and then we add 5 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 a negative 2t plus 5 is equal to 13 so let's do that negative 2t plus 5 is equal to 13 well we can subtract 5 from both sides I'm just trying to isolate the T on the left hand side so subtract negative 5 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 5 is 8 and on the left hand side you still have your negative 2t so you have negative 2t is equal to 8 now to just have a T on the left hand side I want to divide both sides by negative 2 and I'm left with t is equal to 8 divided by negative 2 is equal to negative 4 so you input negative 4 you input negative 4 into this function into this function and it will output 13 or we could write that F of negative 4 is equal to 13 but this is what they're looking for this is the input value negative 4 is the input value for which f of T is equal to 13 f of negative 4 is equal to 13