Properties of Functions

9000033703

Level: 
B
Find the domain of the following function. \[ f\colon y = \frac{x} {\sqrt{4x^{2 } - 9}} \]
\(\left (-\infty ,-\frac{3} {2}\right )\cup \left (\frac{3} {2},\infty \right )\)
\(\mathbb{R}\)
\(\mathbb{R}\setminus \left \{-\frac{3} {2}, \frac{3} {2}\right \}\)
\(\left (-\frac{3} {2}, \frac{3} {2}\right )\)
\(\left [ -\frac{3} {2}, \frac{3} {2}\right ] \)
\(\left (-\infty ,-\frac{3} {2}\right ] \cup \left [ \frac{3} {2},\infty \right )\)

9000021808

Level: 
B
Find the domain of the following function. \[ f(x) = \sqrt{\frac{(x - 3)(x + 2)} {(1 - x)(3 - x)}} \]
\(\mathop{\mathrm{Dom}}(f) = (-\infty ,-2] \cup (1,3)\cup (3,\infty )\)
\(\mathop{\mathrm{Dom}}(f) = (-\infty ,-2)\cup (1,3)\)
\(\mathop{\mathrm{Dom}}(f) = (-\infty ,-2] \cup (1,\infty )\)
\(\mathop{\mathrm{Dom}}(f) =[ -2,1)\cup (3,\infty )\)

9000010608

Level: 
C
Identify a function which is a possible inverse to the function graphed in the picture.
\(y = x^{3}\), \(x\in (-\infty ,\infty )\)
\(y = x^{-3}\), \(x\in (-2,2)\)
\(y = x^{\frac{1} {3} }\), \(x\in (0,\infty )\)
\(y = -x^{\frac{1} {3} }\), \(x\in (-\infty ,\infty )\)
\(y = 8x\), \(x\in (-\infty ,\infty )\)
\(y = -4x\), \(x\in (-\infty ,\infty )\)

9000010609

Level: 
C
Identify a function which is a possible inverse to the function graphed in the picture.
\(y = x^{-1}\), \(x\in (0,\infty )\)
\(y = x\), \(x\in (0,\infty )\)
\(y = -x\), \(x\in (0,\infty )\)
\(y = -x^{-1}\), \(x\in (0,\infty )\)
\(y = x^{2}\), \(x\in (0,\infty )\)
\(y = -x^{2}\), \(x\in (0,\infty )\)

9000010610

Level: 
C
Identify a function which is a possible inverse to the function graphed in the picture.
\(y = x^{2}\), \(x\in (-\infty ,0] \)
\(y = x^{-2}\), \(x\in (-\infty ,0] \)
\(y = -x^{2}\), \(x\in [ 0,\infty )\)
\(y = x^{\frac{1} {2} }\), \(x\in [ 0,\infty )\)
\(y = -x^{\frac{1} {2} }\), \(x\in [ 0,\infty )\)
\(y = -2x\), \(x\in (-\infty ,0] \)