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REY [17]
2 years ago
13

For the function f(x) = x2 ­ -12, find (f o f­-1)(4) A. 0 B. 4 C. 10 D. 6

Mathematics
1 answer:
slega [8]2 years ago
5 0

We actually don't need to do any computation. By definition, the inverse function f^{-1} changes the role of input and output. So, if a function f maps x onto y, the inverse function maps y onto x.

You have to think like this: if the function makes a step further, the inverse function makes that same step back.

This means that the composition f \circ f^{-1} is always the identity function f(x) = x. In fact,

(f\circ f^{-1})(x) = f(f^{-1}(x)) = x

So, for every function, you have

(f\circ f^{-1})(4) = f(f^{-1}(4)) = 4

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