Test 3
1.
\(f(x)=x^2-4\)
What is the widest domain of f in the real numbers?
A) \((-2,2)\)B) \((2,\infty)\)C) \((-\infty,-2)\)D) \((-3,3)\)E) \(\mathbb R\)
2.
\(f(x)=\samefrac{x-4}{x-2}\)
What is the widest domain of f in the real numbers?
A) \((2,\infty)\)B) \((-\infty,-2)\)C) \(\mathbb R\)D) \(\mathbb R\setminus\{1\}\)E) \(\mathbb R\setminus\{2\}\)
3.
\(f(x)=\samefrac{x^2-9}{x^2-2x-3}\)
What is the widest domain of f in the real numbers?
A) \(\mathbb R\setminus\{1\}\)B) \(\mathbb R\setminus\{-1,5\}\)C) \((-1,5)\)D) \(\mathbb R\setminus\{-1\}\)E) \(\mathbb R\setminus\{-1,3\}\)
4.
\(f(x)=\samefrac{2x-5}{x^2+x+4}\)
What is the widest domain of f in the real numbers?
A) \(\mathbb R\)B) \(\mathbb R\setminus\{-4,2\}\)C) \((-2,4)\)D) \((-2,1)\)E) \(\varnothing\)
5.
\(f:\mathbb R\to\mathbb R\)
\(f(x)=\samefrac{3x+1}{x^2-bx+b+3}\)
In which interval can b take values?
A) \((-6,2)\)B) \((-2,6)\)C) \((2,6)\)D) \((-2,4)\)E) \((1,4)\)
6.
\(f(x)=\sqrt[5]{x^2-2x-8}\)
What is the widest domain of f in the real numbers?
A) \((-2,4)\)B) \((2,4)\)C) \(\mathbb R\)D) \((-4,2)\)E) \(\mathbb R\setminus\{-2,4\}\)
7.
\(f(x)=\sqrt{9-x^2}\)
What is the widest domain of f in the real numbers?
A) \((-3,3)\)B) \([-3,3]\)C) \([3,\infty)\)D) \((-\infty,3)\)E) \(\varnothing\)
8.
\(f:A\to\mathbb R\)
\(f(x)=\sqrt[8]{\samefrac{(x-2)^2}{4x-x^2}}\)
What is the sum of the integer members of A?
A) \(14\)B) \(10\)C) \(6\)D) \(4\)E) \(2\)