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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The compositions $f(g(x))$ and $g(f(x))$ both simplify to $x$, indicating that $f$ and $g$ are indeed inverse functions of each other.

Determine Algebraically Whether F and G Are Inverse Functions g(x)=x+35g ( x ) = \frac { x + 3 } { 5 }g(x)=5x+3​

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