Question

If function `f(x)={((x^2-9)/(x-3), ",when "xne3),(k, ",when "x =3):}` is continuous at x = 3, then the value of k will be ______.

Options

• -1

• 6

• -3

• -2

Answer 1

If function `f(x)={((x^2-9)/(x-3), ",when "xne3),(k, ",when "x =3):}` is continuous at x = 3, then the value of k will be 6.

Explanation:

Since, f(x) is continuous at x = 3.

`therefore f(1)=lim_(x->3)f(x)`

`=>k=lim_(x->3)(x^2-9)/(x-3)`

`=>k=lim_(x->3)(x+3)`

⇒ k = 6