SOLUTION: Find the value of c such that the domain of f(x) = sqrt(c-x^2) is [-13,13]

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Question 698798: Find the value of c such that the domain of f(x) = sqrt(c-x^2) is [-13,13]
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+sqrt%28c-x%5E2%29 ....if the point is at [-13,13], means x=-13 and f%28x%29=13; so, we will plug it in formula
f%28x%29+=+sqrt%28c-x%5E2%29 and solve for c
13+=+sqrt%28c-%28-13%29%5E2%29
13+=+sqrt%28c-169%29...both sides raise to power of two
13%5E2+=+%28sqrt%28c-169%29%29%5E2
169+=+c-169
169%2B169+=+c
338=+c
so, you have a function f%28x%29+=+sqrt%28338-x%5E2%29 that has a solution set x=-13 and f%28x%29=13
let's see it on a graph:

+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C+sqrt%28338-x%5E2%29-13%29+