Which function has a removable discontinuity?

A. p(x)= (x+2)/(x^2-x-2)
B. ƒ(x)= 5x/x-x^2
C. g(x)=2x-1/x
D. h(x)=x^2-x+2/x+1

Question

Which function has a removable discontinuity?

A. p(x)= (x+2)/(x^2-x-2)
B. ƒ(x)= 5x/x-x^2
C. g(x)=2x-1/x
D. h(x)=x^2-x+2/x+1

jim_thompson5910 · Answer

They want to know which graph has a hole. Notice that the denominator in choice B factors to x(x-1) and the 'x' terms cancel leaving you with$$f(x)=\frac{5}{x-1}$$ This function has a discontinuity at x=1 (to avoid division by zero) but we must also throw in that x can't equal zero as well to ensure that it is equivalent to the original equation in choice B.


So the answer is choice B.

anonymous · Answer

thanks