Question

If f(2)=10 and f(7)=14, evaluate f-¹(14)

Answer 1

Answer:  $f^{-1}(14) = 7$

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Explanation:

Focus only on the f(7) = 14

Apply the inverse function to both sides

$f(7) = 14\\\\f^{-1}(f(7)) = f^{-1}(14)\\\\7 = f^{-1}(14)\\\\f^{-1}(14) = 7$

In the third step, I used the rule that $f^{-1}(f(x)) = x$

That rule says the inverse function undoes the original function. That's why we get the original input back.

Put another way: The f(7) = 14 says "the input 7 leads to the output 14". When computing the inverse, we go in reverse of this process.

The f(2) = 10 is never used at all. It seems to be filler or a distraction.