Answer: f(-6)=-12
Step-by-step explanation:
We are given a function : [tex]f(x) =\dfrac{ x^2-36 }{x+6}[/tex] which is continuous at x = -6.
Now, using identity [tex]a^2-b^2=(a+b)(a-b)[/tex] , we have
[tex]x^2-36=x^2-6^2=(x+6)(x-6)[/tex]
Replace [tex]x^2-36\text{ by }(x+6)(x-6)[/tex] in the given function:-
[tex]f(x) =\dfrac{ x^2-36 }{x+6}=\dfrac{(x+6)(x-6)}{x+6}[/tex]
Cancel (x+6) from numerator and denominator , we get
[tex]f(x)=x-6[/tex]
Now,[tex]f(-6)=-6-6=-12[/tex]
Hence, f(-6)=-12
