B

9000020901

Level: 
B
The solution of the given set of equations can be interpreted as the intersection of the curves shown in the figure. Find the solution of the system in \(\mathbb{R}\times \mathbb{R}\). \[ \begin{alignedat}{80} &2x^{2} & - &3y &^{2} & = 2 &4 & & & & & & & & \\ &2x & - &3y & & = &0 & & & & & & & & \\\end{alignedat}\]
\([-6,-4],\ [6,4]\)
\([-6,-4]\)
\([6,4]\)
no solution

9000020902

Level: 
B
The solution of the given set of equations can be interpreted as the intersection of the curves shown in the figure. Find the solution of the system in \(\mathbb{R}\times \mathbb{R}\). \[ \begin{alignedat}{80} &4x^{2} & + &y &^{2} & = &20 & & & & & & & & & \\ &2x & + &y & & = &6 & & & & & & & & & \\\end{alignedat}\]
\([1,4],\ [2,2]\)
\([2,2]\)
\([1,4]\)
no solution

9000014206

Level: 
B
Find the domain \(\mathrm{Dom}(f)\) and range \(\mathop{\mathrm{Ran}}(f)\) of the function \(f(x) = \frac{2+x} {x+4}\).
\begin{align*} \mathrm{Dom}(f) &= (-\infty ,-4)\cup (-4,\infty ),\\ \mathop{\mathrm{Ran}}(f) &= (-\infty ,1)\cup (1,\infty ) \end{align*}
\begin{align*} \mathrm{Dom}(f) &= (-\infty ,4)\cup (4,\infty ), \\ \mathop{\mathrm{Ran}}(f) &= (-\infty ,1)\cup (1,\infty ) \end{align*}
\begin{align*} \mathrm{Dom}(f) &= (-\infty ,2)\cup (2,\infty ),\\ \mathop{\mathrm{Ran}}(f) &= (-\infty ,4)\cup (4,\infty ) \end{align*}
\begin{align*} \mathrm{Dom}(f) &= (-\infty ,4)\cup (4,\infty ), \\ \mathop{\mathrm{Ran}}(f) &= (-\infty ,2)\cup (2,\infty ) \end{align*}