Sketch the graphs of inverse functions

f ( x ) = x ^ { 5 } - 2 , f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x + 2 }

in the same coordinate plane and show that the graphs are reflections of each other in the line

y = x

A) $Sketch the graphs of inverse functions f ( x ) = x ^ { 5 } - 2 , f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x + 2 } in the same coordinate plane and show that the graphs are reflections of each other in the line y = x A) \begin{array} { l l r r } x & - 1 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 4 & - 2 & - 1 \\ f ^ { - 1 } ( x ) & - 1 & 0 & 1 \end{array} B) \begin{array} { l lrr } x & - 1 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 3 & - 2 & -1\\ f ^ { - 1 } ( x ) & - 1 & 2 & 1 \end{array} C) \begin{array} { l r rr } x & 0 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 3 & - 2 & -1\\ f ^ { - 1 } ( x ) & - 1 & 0 & 1 \end{array} D) \begin{array} { l l rr } x & - 1 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 3 & - 2 & -1\\ f ^ { - 1 } ( x ) & - 1 & 0 & 1 \end{array} E) \begin{array}{llrr} x & -1 & 0 & -1 \\ f(x) & -3 & -2 & -1 \\\\ x & -3& 2& -1 \\ f^{-1}(x) & -1 & -2 & 1 \end{array}$

\begin{array} { l l r r } x & - 1 & 0 & 1 \\f ( x ) & - 3 & - 2 & - 1 \\\\x & - 4 & - 2 & - 1 \\f ^ { - 1 } ( x ) & - 1 & 0 & 1\end{array}

B) $Sketch the graphs of inverse functions f ( x ) = x ^ { 5 } - 2 , f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x + 2 } in the same coordinate plane and show that the graphs are reflections of each other in the line y = x A) \begin{array} { l l r r } x & - 1 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 4 & - 2 & - 1 \\ f ^ { - 1 } ( x ) & - 1 & 0 & 1 \end{array} B) \begin{array} { l lrr } x & - 1 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 3 & - 2 & -1\\ f ^ { - 1 } ( x ) & - 1 & 2 & 1 \end{array} C) \begin{array} { l r rr } x & 0 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 3 & - 2 & -1\\ f ^ { - 1 } ( x ) & - 1 & 0 & 1 \end{array} D) \begin{array} { l l rr } x & - 1 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 3 & - 2 & -1\\ f ^ { - 1 } ( x ) & - 1 & 0 & 1 \end{array} E) \begin{array}{llrr} x & -1 & 0 & -1 \\ f(x) & -3 & -2 & -1 \\\\ x & -3& 2& -1 \\ f^{-1}(x) & -1 & -2 & 1 \end{array}$

\begin{array} { l lrr } x & - 1 & 0 & 1 \\f ( x ) & - 3 & - 2 & - 1 \\\\x & - 3 & - 2 & -1\\f ^ { - 1 } ( x ) & - 1 & 2 & 1\end{array}

C) $Sketch the graphs of inverse functions f ( x ) = x ^ { 5 } - 2 , f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x + 2 } in the same coordinate plane and show that the graphs are reflections of each other in the line y = x A) \begin{array} { l l r r } x & - 1 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 4 & - 2 & - 1 \\ f ^ { - 1 } ( x ) & - 1 & 0 & 1 \end{array} B) \begin{array} { l lrr } x & - 1 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 3 & - 2 & -1\\ f ^ { - 1 } ( x ) & - 1 & 2 & 1 \end{array} C) \begin{array} { l r rr } x & 0 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 3 & - 2 & -1\\ f ^ { - 1 } ( x ) & - 1 & 0 & 1 \end{array} D) \begin{array} { l l rr } x & - 1 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 3 & - 2 & -1\\ f ^ { - 1 } ( x ) & - 1 & 0 & 1 \end{array} E) \begin{array}{llrr} x & -1 & 0 & -1 \\ f(x) & -3 & -2 & -1 \\\\ x & -3& 2& -1 \\ f^{-1}(x) & -1 & -2 & 1 \end{array}$

\begin{array} { l r rr } x & 0 & 0 & 1 \\f ( x ) & - 3 & - 2 & - 1 \\\\x & - 3 & - 2 & -1\\f ^ { - 1 } ( x ) & - 1 & 0 & 1\end{array}

D) $Sketch the graphs of inverse functions f ( x ) = x ^ { 5 } - 2 , f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x + 2 } in the same coordinate plane and show that the graphs are reflections of each other in the line y = x A) \begin{array} { l l r r } x & - 1 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 4 & - 2 & - 1 \\ f ^ { - 1 } ( x ) & - 1 & 0 & 1 \end{array} B) \begin{array} { l lrr } x & - 1 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 3 & - 2 & -1\\ f ^ { - 1 } ( x ) & - 1 & 2 & 1 \end{array} C) \begin{array} { l r rr } x & 0 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 3 & - 2 & -1\\ f ^ { - 1 } ( x ) & - 1 & 0 & 1 \end{array} D) \begin{array} { l l rr } x & - 1 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 3 & - 2 & -1\\ f ^ { - 1 } ( x ) & - 1 & 0 & 1 \end{array} E) \begin{array}{llrr} x & -1 & 0 & -1 \\ f(x) & -3 & -2 & -1 \\\\ x & -3& 2& -1 \\ f^{-1}(x) & -1 & -2 & 1 \end{array}$

\begin{array} { l l rr } x & - 1 & 0 & 1 \\f ( x ) & - 3 & - 2 & - 1 \\\\x & - 3 & - 2 & -1\\f ^ { - 1 } ( x ) & - 1 & 0 & 1\end{array}

E) $Sketch the graphs of inverse functions f ( x ) = x ^ { 5 } - 2 , f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x + 2 } in the same coordinate plane and show that the graphs are reflections of each other in the line y = x A) \begin{array} { l l r r } x & - 1 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 4 & - 2 & - 1 \\ f ^ { - 1 } ( x ) & - 1 & 0 & 1 \end{array} B) \begin{array} { l lrr } x & - 1 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 3 & - 2 & -1\\ f ^ { - 1 } ( x ) & - 1 & 2 & 1 \end{array} C) \begin{array} { l r rr } x & 0 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 3 & - 2 & -1\\ f ^ { - 1 } ( x ) & - 1 & 0 & 1 \end{array} D) \begin{array} { l l rr } x & - 1 & 0 & 1 \\ f ( x ) & - 3 & - 2 & - 1 \\\\ x & - 3 & - 2 & -1\\ f ^ { - 1 } ( x ) & - 1 & 0 & 1 \end{array} E) \begin{array}{llrr} x & -1 & 0 & -1 \\ f(x) & -3 & -2 & -1 \\\\ x & -3& 2& -1 \\ f^{-1}(x) & -1 & -2 & 1 \end{array}$

\begin{array}{llrr}x & -1 & 0 & -1 \\f(x) & -3 & -2 & -1 \\\\x & -3& 2& -1 \\f^{-1}(x) & -1 & -2 & 1\end{array}

Apply the Inverse Property of Logarithmic or Exponential Functions to Simplify

Multiple Choice

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