Properties of Functions

2000005202

Level: 
C
From the given functions select a function \(f\) so that its inverse function \(f^{-1}\) has the graph shown in the picture.
\( f(x) = \sqrt{x+1},~x\in[ -1,\infty) \)
\( f(x) = x^2-1,~x\in (-\infty,0]\)
\( f(x) = \frac{1}{\sqrt{x-1}},~x\in[ -1,\infty) \)
\( f(x) = x^2-1,~x\in\ \mathbb{R} \)

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.
\(y = x^{2}\), \(x\in (-\infty ,0] \)
\(y = x^{-2}\), \(x\in (-\infty ,0] \)
\(y = -x^{2}\), \(x\in [ 0,\infty )\)
\(y = x^{\frac{1} {2} }\), \(x\in [ 0,\infty )\)
\(y = -x^{\frac{1} {2} }\), \(x\in [ 0,\infty )\)
\(y = -2x\), \(x\in (-\infty ,0] \)