# The function $f(x) = \frac{log(1 + ax)-log(1 – bx)}{x}$ is not defined at x= 0. The value which should be assigned

Q: The function $f(x) = \frac{log(1 + ax)-log(1 – bx)}{x}$ is not defined at x= 0. The value which should be assigned to f at x = 0, so that it is continuous at x = 0 is

(A) a – b

(B) a + b

(C) log a + log b

(D) none of these

Sol: $f(x) = a[\frac{log(1+ax)}{ax}] + b[\frac{log(1-bx)}{-bx}]$

So , $\large \lim_{x \rightarrow 0}f(x) = a .1 + b.1 = (a+b) = f(0)$

Hence (B) is the correct answer.