Determine Algebraically Whether F and G Are Inverse Functions $f ( x ) = \sqrt { x + 6 }$

question 30

Multiple Choice

Determine algebraically whether f and g are inverse functions. $f ( x ) = \sqrt { x + 6 }$ g(x) = x² - 6,x ? 0

• A)Yes,f and g are inverse functions. \(f ( g ( x ) ) = f \left( x ^ { 2 } - 6 \right) = \sqrt { \left( x ^ { 2 } - 6 \right) + 6 } = \sqrt { x ^ { 2 } } = x\) \(g ( f ( x ) ) = g ( \sqrt { x + 6 } ) = ( \sqrt { x + 6 } ) ^ { 2 } - 6 = x + 6 - 6 = x\)
• B)No,f and g are not inverse functions. \(f ( g ( x ) ) = f \left( x ^ { 2 } - 6 \right) = \sqrt { \left( x ^ { 2 } - 6 \right) + 6 } = \sqrt { x ^ { 2 } } = x\) \(g ( f ( x ) ) = g ( \sqrt { x + 6 } ) = ( \sqrt { x + 6 } ) ^ { 2 } - 6 = - x + 6 - 6 = - x\)

Identify the stages of human development and their associated challenges according to Erikson's theory.

Distinguish between different research approaches in developmental psychology (e.g., cross-sectional vs. longitudinal).

Grasp how psychological theories explain changes from conception to death.

Analyze the impact of biological maturation on development.

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Undue Fatigue

Excessive tiredness not proportionate to the activity level, often a sign of underlying health issues or overexertion.

Prolonged Period

An extended length of time, usually longer than typical or expected.

Dynamic Training

A form of exercise that involves movement and activities designed to improve strength, speed, and functional mobility through variable resistance.

Muscle Contraction

The physiological process where muscles respond to stimuli and change in tension, leading to movement or maintenance of posture.