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If f(x) = x^2-36/x+6 is continuous at x = –6, find f(–6).

1 Answer

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Answer: f(-6)=-12

Explanation:

We are given a function :
f(x) =( x^2-36 )/(x+6) which is continuous at x = -6.

Now, using identity
a^2-b^2=(a+b)(a-b) , we have


x^2-36=x^2-6^2=(x+6)(x-6)

Replace
x^2-36\text{ by }(x+6)(x-6) in the given function:-


f(x) =( x^2-36 )/(x+6)=((x+6)(x-6))/(x+6)

Cancel (x+6) from numerator and denominator , we get


f(x)=x-6

Now,
f(-6)=-6-6=-12

Hence, f(-6)=-12

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