f(x) = [tex]\frac{4x+1}{5x}[/tex] g(x) = [tex]\frac{5x-1}{x+4}[/tex]
g⁻¹(x): x = [tex]\frac{5y-1}{y+4}[/tex]
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
[tex]\frac{4x+1}{5 - x}[/tex] = 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)
