Domains of functions

F(x)=x²-7x and g(x)=5-x²
Domain of (fg)(x) is. .. . .
Domain of (f/g)(x). ..

Result

a = (Correct answer is: R)
b = (Correct answer is: R - { x1,x2 })

Solution:

$a=R$

$$\begin{gathered} g(x)<>0 \\ 5-x^2=0 \\ 5-x^2=0 \\ -x^2+5=0 \\ {x}^2-5=0 \\ a=1;b=0;c=-5 \\ D=b^2-4ac=0^2-4\cdot 1\cdot (-5)=20 \\ D>0 \\ {x}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{\pm \sqrt{20}}{2}}={\displaystyle \frac{\pm 2\sqrt{5}}{2}} \\ {x}_{1,2}=\pm \sqrt{5}=\pm 2.2360679775 \\ {x}_1=\sqrt{5}=2.2360679775 \\ {x}_2=-\sqrt{5}=-2.2360679775 \\ \text{ Factored form of the equation: } \\ (x-2.2360679775)(x+2.2360679775)=0 \\ b=R-x_1,x_2 \end{gathered}$$

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