Let Me Find f ( x ) First
If f ( x 3 ) = 3 6 is true for all real x , what is f ( x 2 ) ?
The answer is 36.
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2 solutions
If f ( x 2 ) = 3 6 ∀ x ∈ R then, f ( x 3 ) = 3 6 ∀ x ∈ R + ∪ { 0 } , but f ( x 3 ) = 3 6 ∀ x ∈ R in general.
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Thank you and I will change this question once again:) it is not supposed to be difficult at all.
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Why must we have f ( − 1 ) = 3 6 ?
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@Calvin Lin – Thank you for pointing out and I changed this problem the third time... I really have learned a lot from this problem!
Smart change by the way!
Well, then you should have mentioned that it is true for all x. From the given statement we know that there is a 'x' such that f ( x 2 ) = 3 6 .
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Thank you very much and I will add it to the question :D
A function that always has an output 36 when you insert anything, is the function f(x) = 36. So, logically, if you insert x^2 instead of x^3, the result will remain 36.
Note that there is NOT a specific value given to x . This means if f ( x 3 ) =36, then f ( a n y t h i n g ) =36. Therefore, our answer to this question is 3 6