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

Question

Quizplus · Accepted Answer

The calculations for both $f(g(x))$ and $g(f(x))$ correctly 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 $g ( x ) = \frac { x + 3 } { 5 }$