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

Algebra ->  Equations -> 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      Log On


   

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) About Me  (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....

h%281%2F3%29=%281%2Fk%29%281%2F3%29%5Ek=%281%2F3%29%5E4

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:

h%281%2F3%29=%281%2F3%29%281%2F3%29%5E3=%281%2F3%29%5E4

Yes, it works.

ANSWER: (A) 3