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Given:
Choose a number between 0 and 20.
If the difference is less than 10 then Eric wins.
Let us x is Eric's number. 0 <u><</u> x <u><</u> 20
If Eric wins. |x -7| < 10
|x-7| < 10 → -10 < x-7 < 10 → -10 + 7 < x - 7 + 7 < 10 + 7 → -3 < x < 17
Taking into account that the number must be given between 0 and 20.
0 <u><</u> x <u><</u> 20
-3 < x < 17
→ 0 < x < 16
Here is how we get the answer....
First, replace f(x) with y . ...
Replace every x with a y and replace every y with an x .
Solve the equation from Step 2 for y . ...
Replace y with f−1(x) f − 1 ( x ) . ...
Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.
