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If f−1(−25)=7 f^{-1}(-25) = 7 , then what is f(7) f(7) ?

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Full solution

Q. If f−1(−25)=7 f^{-1}(-25) = 7 , then what is f(7) f(7) ?
  1. Given information: We are given that f−1(−25)=7f^{-1}(-25) = 7, which means that when the inverse function of ff is applied to −25-25, the result is 77. This implies that applying the function ff to 77 should give us −25-25, because the function and its inverse undo each other.
  2. Implication of given information: Since we know that applying ff to 77 should give us the value that, when the inverse function is applied, gives us 77, we can conclude that f(7)=−25f(7) = -25. This is by the definition of inverse functions: if f−1(x)=yf^{-1}(x) = y, then f(y)=xf(y) = x.

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