ONE EIGHTH CONTEST 2025
Presbyterian Boys' Sec. School - 55 points
Oti Boateng SHS - 35 points
T.I. AMASS, Kumasi - 34 points
ONE EIGHTH CONTEST 2025
Our Lady of Grace SHS - 56 points
Bishop Herman College - 39 points
Ejisuman SHS - 27 points
ONE EIGHTH CONTEST 2025
GSTS - 50 points
Nkwatia Presbyterian SHS - 45 points
Ashaiman SHS - 28 points
ROUND 2
QUESTION
Find the domain of the function $f(x)=\sqrt{x^{2}+3}$.
ANSWER: $\{x:x\in\mathbb{R}\}$
SOLUTION
$y=\sqrt{x^{2}+3}$
The expression under the square root must be non-negative.
Since $x^{2}\geq0$ for every real $x$:
$x^{2}+3\geq3$
So $x^{2}+3$ is always positive, and the function is defined for every real number.
$\{x:x\in\mathbb{R}\}$
PRACTICE QUESTIONS
1. Find the domain of the function $f(x)=\sqrt{x^{2}+5}$.
ANSWER: $\{x:x\in\mathbb{R}\}$
SOLUTION
The expression under the square root must be non-negative:
$x^{2}+5\geq0$
The discriminant is negative and the coefficient of $x^2$ is positive, so $x^{2}+5\gt0$ for every real $x$.
The function is defined for every real number.
2. Find the domain of the function $f(x)=\sqrt{x^{2}+9}$.
ANSWER: $\{x:x\in\mathbb{R}\}$
SOLUTION
The expression under the square root must be non-negative:
$x^{2}+9\geq0$
The discriminant is negative and the coefficient of $x^2$ is positive, so $x^{2}+9\gt0$ for every real $x$.
The function is defined for every real number.
3. Find the domain of the function $f(x)=\sqrt{x^{2}+2x+5}$.
ANSWER: $\{x:x\in\mathbb{R}\}$
SOLUTION
The expression under the square root must be non-negative:
$x^{2}+2x+5\geq0$
The discriminant is negative and the coefficient of $x^2$ is positive, so $x^{2}+2x+5\gt0$ for every real $x$.
The function is defined for every real number.
4. Find the domain of the function $f(x)=\sqrt{3x^{2}+1}$.
ANSWER: $\{x:x\in\mathbb{R}\}$
SOLUTION
The expression under the square root must be non-negative:
$3x^{2}+1\geq0$
The discriminant is negative and the coefficient of $x^2$ is positive, so $3x^{2}+1\gt0$ for every real $x$.
The function is defined for every real number.
5. Find the domain of the function $f(x)=\sqrt{x^{2}-6x+10}$.
ANSWER: $\{x:x\in\mathbb{R}\}$
SOLUTION
The expression under the square root must be non-negative:
$x^{2}-6x+10\geq0$
The discriminant is negative and the coefficient of $x^2$ is positive, so $x^{2}-6x+10\gt0$ for every real $x$.
The function is defined for every real number.
6. Find the domain of the function $f(x)=\sqrt{2x^{2}+x+3}$.
ANSWER: $\{x:x\in\mathbb{R}\}$
SOLUTION
The expression under the square root must be non-negative:
$2x^{2}+x+3\geq0$
The discriminant is negative and the coefficient of $x^2$ is positive, so $2x^{2}+x+3\gt0$ for every real $x$.
The function is defined for every real number.