Question

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

• A. a - b
• B. a + b
• C. log a + log b
• D. log a - log b

Answer 1

The correct option is B a + b

Since limit of a function is a + b as x $\to$ 0. {We can apply L'Hospital rule to find the limit easily.}
Therefore it to be continuous at x= 0, its value must be (a + b) at x = 0
$\Rightarrow$ f(0) = a + b