Question

Given the function

f(x)
, find its domain.

f(x)= (4x+17)/ x^2-10x+21

The domain is all real numbers except
x=

If there is more than one answer, write it as a list, using commas to separate your answers.

Answer 1

The domain is all real numbers except

x = 3 and x = 7.

Explanation:

We know that in a fraction the denominator must be different from 0.

Therefore:

`f(x)=(4x+17)/(x^2-10x+21)\to\ D:x^2-10x+21\\eq0\\\\x^2-7x-3x+21\\eq0\\\\x(x-7)-3(x-7)\\eq0\\\\(x-7)(x-3)\\eq0\iff x-7\\eq0\ \wedge\ x-3\\eq0\\\\x-7\\eq0\qquad\text{add 7 to both sides}\\x\\eq7\\\\x-3\\eq0\qquad\text{add 3 to both sides}\\x\\eq3`