Determine Algebraically Whether F and G Are Inverse Functions $g ( x ) = \frac { x + 3 } { 5 }$

question 3

Multiple Choice

Determine algebraically whether f and g are inverse functions. f(x) = 5x - 3 $g ( x ) = \frac { x + 3 } { 5 }$

• A)Yes,f and g are inverse functions. \(f ( g ( x ) ) = f \left( \frac { x + 3 } { 5 } \right) = 5 \left( \frac { x + 3 } { 5 } \right) - 3 = x + 3 - 3 = x\) \(g ( f ( x ) ) = g ( 5 x - 3 ) = \frac { 5 x - 3 + 3 } { 5 } = \frac { 5 x } { 5 } = x\)
• B)No,f and g are not inverse functions. \(f ( g ( x ) ) = f \left( \frac { x + 3 } { 5 } \right) = 5 \left( \frac { x + 3 } { 5 } \right) - 3 = x + 3 - 3 = x\) \(g ( f ( x ) ) = g ( 5 x - 3 ) = \frac { 5 x - 3 + 3 } { 5 } = \frac { 5 x } { 5 } = - x\)

Recognize the transformative effect of the Civil War on American society, politics, and the economy.

Understand the effects of the Civil War on African-Americans, including their participation in the war and the immediate aftermath.

Examine the advancements and challenges in medical care, communication, and warfare technology during the Civil War.

Grasp the global perception of the Civil War and its key figures post-war.

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