A student recognizes that the function f(x)=(x2+4x+3) / (x+1) can be simplified as:

Question

A student recognizes that the function f(x)=(x²+4x+3) / (x+1) can be simplified as:

f(x)=(x²+4x+3) / (x+1) = (x+1)(x+3) / (x+1) = x+3

SInce y=x+3 is a line with slope of 1, the student makes the following conclusions:

f ' (-2) = 1, f ' (-1) = 1, f ' (0) = 1, f ' (1) = 1,

Where did the student make error?

Answer 1

the error is saying f'(-1) = 1

x cannot = -1 as it makes the original function undefined, with division by zero

while f(x) is a line with slope = 1, it has a discontinuity at the point (-1,2)

f(x) is a line but with a point missing where x=-1

Answer 2

The function does not have a derivative where it is not defined or continuous. The similar function does not have the same domain as the original.