Question

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

Answer 1

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