SOLUTION: Let the function h be defined by h(x) = (1/k) * x^k for some non-zero constant k. If h(1/3) = (1/3)^4 then what is the value of k? (A) 3 (B) 1/3 (C) 4 (D) 1/4 (E) 3/4

Question 1202590: Let the function h be defined by h(x) = (1/k) * x^k for some
non-zero constant k. If h(1/3) = (1/3)^4 then what is the
value of k?
(A) 3
(B) 1/3
(C) 4
(D) 1/4
(E) 3/4
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

If this were a problem on a test, probably the fastest path to the answer would be to try the answer choices to see which one works.

Using formal algebra, or rather just logical reasoning....

Since the right hand side is a pure exponential, the only way the left hand side can be equal to the right hand side is if k is 3:

Yes, it works.

ANSWER: (A) 3

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