Sketch the Graphs of Inverse Functions $f ( x ) = x ^ { 5 } - 2 , f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x + 2 }$

question 20

Multiple Choice

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

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Definitions:

Cognitive Model

A framework in psychology that describes how thoughts, feelings, and behaviors interact and influence each other.

Physical Processes

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A systematic technique in counseling intended to address negative emotions, behaviors, and beliefs through a goal-specific, orderly approach.

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Actions, thoughts, or emotions that deviate significantly from cultural norms or expectations, often leading to distress or impairment in daily functioning.