Mathematics

Problem

Let

f

have a removable discontinuity at

x=a

(that is,

\lim_{x\to a}f(x)

exists and is finite, but

f(a)

is not equal to this limit or is undefined). Which of the following transformations is most likely to introduce an infinite discontinuity at

x=a

? a)

g(x)=|f(x)|

g(x)=\dfrac{1}{f(x)}

g(x)=\dfrac{f(x)}{x-a}

g(x)=\ln\bigl(f(x)\bigr)