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

question 90

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. \[f ( g ( x ) ) = f \left( \frac { x + 3 } { 5 } \right) = 5 \left( \frac { x + 3 } { 5 } \right) - 3 = x + 3 - 3 = x\] \[g ( f ( x ) ) = g ( 5 x - 3 ) = \frac { 5 x - 3 + 3 } { 5 } = \frac { 5 x } { 5 } = - x\]

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