Question

Medal for the correct answer!
Given the function f(x) = 6(x+2) − 3, solve for the inverse function when x = 21.

−45

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Answer 1

Kind of strangely worded, lol.... I would take "solve for the inverse function" to mean FIND the FUNCTION that is the inverse of f(x), but that isn't what they want, since the answers are numerical, and not functions.

So what you need to remember is that the inverse function and the original have "swapped" domains and ranges. That is, when you evaluate the inverse function \(f^{-1}(x)\), your INPUT x is a value in the RANGE of the function f(x), and your OUTPUT y is the value IN THE DOMAIN of f(x) that results in that value as the output.

So, since you are looking for "the inverse function when x = 21", I would interpret that to mean "what is \(f^{-1}(21)\)?" Well, \(f^{-1}(21)\) has to be the value in the DOMAIN of f that gives you the value 21 in the RANGE of f, e.g. for what x is f(x)=21?

So solve: \(21= 6(x+2) − 3\) and that should be your answer.