Question

Given the function

Answer 1

Answer:

The domain is all real numbers except

x = 3 and x = 7.

Step-by-step explanation:

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

Therefore:

$f(x)=\dfrac{4x+17}{x^2-10x+21}\to\ D:x^2-10x+21\neq0\\\\x^2-7x-3x+21\neq0\\\\x(x-7)-3(x-7)\neq0\\\\(x-7)(x-3)\neq0\iff x-7\neq0\ \wedge\ x-3\neq0\\\\x-7\neq0\qquad\text{add 7 to both sides}\\x\neq7\\\\x-3\neq0\qquad\text{add 3 to both sides}\\x\neq3$