Question

determine if f(x)=4x+1/x*5 and g(x)=5x-1/x+4 are inverses of each other. if they are not inverses, explain why.

Answer 1

f(x) = $\frac{4x+1}{5x}$                     g(x) = $\frac{5x-1}{x+4}$

g⁻¹(x): x = $\frac{5y-1}{y+4}$

       x(y + 4) = 5y - 1           multiplied both sides by y + 4

       xy + 4x = 5y - 1           distributed x into y + 4 on left side

  xy + 4x + 1 = 5y                added 1 to both sides

          4x + 1 = 5y - xy          subtracted xy from both sides

           4x + 1 = y(5 - x)         factored y on the right side

           $\frac{4x+1}{5 - x}$ = y         divided 5 - x from both sides

f(x) ≠ g⁻¹(x)  so they are not inverses of each other

Answer: NOT INVERSES because f(x) ≠ g⁻¹(x)