Question #29f86

2 Answers
Douglas K.
Feb 5, 2018

f^-1(-12) = -8f−1(−12)=−8

Explanation:

The inverse of a function, f^-1(y)f−1(y), reverses what the function, f(x)f(x), does.

If y = f(x)y=f(x), then f^-1(y)=xf−1(y)=x

Making this fit the context of your question

We are given that f(-8) = -12f(−8)=−12

The standard notation is y = f(x)y=f(x), therefore, y =-12y=−12 in this case. Then, using f^-1(y) = xf−1(y)=x gives us f^-1(-12) = -8f−1(−12)=−8

The Legend
Feb 5, 2018

You would figure out f(x)f(x), then find f(-12)f(−12) and raise it to the -1−1 power, a.k.a. find the reciprocal.

Explanation:

If f(-8)=-12f(−8)=−12, then what is f(x)f(x)? Well, -8-4 = -12−8−4=−12, so f(x)=x-4f(x)=x−4. Then if x=-12x=−12, f(x)=x-4 = f(-12)= -12-4 = -16f(x)=x−4=f(−12)=−12−4=−16, so f(-12)= -16f(−12)=−16. Are we done? Nope. We are asked to find f^-1(-12)f−1(−12), not just f(-12)f(−12). That means we raise f(-12)f(−12) to the power of -1−1.When you raise something to the -1−1 power, you find the reciprocal. This is easy: just turn it into a fraction and flip it. -16= -16/1−16=−161. Flip the fraction and you get -1/16−116. So if f(-8)=-12f(−8)=−12, then

f^-1(-12)=-16f−1(−12)=−16. We have our answer.

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