Question

Which function has a removable discontinuity at x = 7? f (x) = StartFraction 3 Over x minus 7 EndFraction f (x) = StartFraction x squared minus 10 x + 21 Over x minus 7 EndFraction f (x) = StartLayout Enlarged left-brace first row negative x, x less-than 7 second row x + 1, x greater-than-or-equal-to 7 EndLayout f (x) = StartLayout Enlarged left-brace first row negative StartFraction x Over x minus 7 EndFraction, x less-than 7 second row x + 1, x greater-than-or-equal-to 7 EndLayout

Answer 1

A function that has a removable discontinuity at x = 7 include the following: B.
`f(x)=(x^(2)-10x+21 )/(x-7)`.

In Mathematics and Geometry, a removable discontinuity is a point on the graph of a function that is considered as undefined or that does not accurately fit the other part of a graph.

Generally speaking, a rational function is undefined when the denominator is equal to zero. This ultimately implies that, we can determined the x-values of discontinuity by evaluating the denominator as follows;

`f(x)=(x^(2)-10x+21 )/(x-7)\\\\f(x)=((x-3)(x-7) )/(x-7)\\\\f(x)=x-3`

x - 7 ≠ 0

x ≠ 7

Based on the answer choices below, functions A, C, and D do not have a limit at x = 7 because it does not exist (DNE).

Complete Question:

Which function has a removable discontinuity at x = 7?