Test 4
1.
\(f(x)=\sqrt{9-|x|}\)
What is the widest domain of f in the real numbers?
A) \((9,\infty)\)B) \((-\infty,-9)\)C) \((-9,9)\)D) \([-9,9]\)E) \((0,9]\)
2.
\(f(x)=\sqrt{6-|2x-4|}\)
What is the widest domain of f in the real numbers?
A) \((-1,5]\)B) \([-1,5]\)C) \([-1,\infty)\)D) \((-\infty,5]\)E) \([5,\infty)\)
3.
\(f(x)=\sqrt{\samefrac{x+4}{2-|x-1|}}\)
What is the widest domain of f in the real numbers?
A) \(\varnothing\)B) \(\mathbb R\)C) \((-1,\infty)\)D) \((2,\infty)\)E) \((-\infty,-4]\cup(-1,3)\)
4.
\(f(x)=\sqrt{-x^2+4x-4}\)
What is the widest domain of f in the real numbers?
A) \(\mathbb R\)B) \(\mathbb R\setminus\{2\}\)C) \(\varnothing\)D) \((-2,2)\)E) \(\{2\}\)
5.
\(f(x)=\log_2(x-4)\)
What is the widest domain of f in the real numbers?
A) \((-\infty,4)\)B) \((1,\infty)\)C) \((4,\infty)\)D) \((2,4]\)E) \([4,\infty)\)
6.
\(f(x)=\log(4x^2-16)\)
What is the widest domain of f in the real numbers?
A) \((-2,\infty)\)B) \((2,\infty)\)C) \((-2,2)\)D) \((-\infty,-2)\)E) \((-\infty,-2)\cup(2,\infty)\)
7.
\(f(x)=\log_{x-2}(-x^2+4x+5)\)
What is the widest domain of f in the real numbers?
A) \((2,5)\)B) \([2,5]\)C) \((-1,5)\)D) \((2,5)\setminus\{3\}\)E) \([2,5)\setminus\{3\}\)
8.
\(f(x)=\log_{\sqrt{x^2-4x+7}}|x-6|\)
What is the widest domain of f in the real numbers?
A) \((6,\infty)\)B) \([6,\infty)\)C) \((-6,6)\)D) \(\mathbb R\)E) \(\mathbb R\setminus\{6\}\)