Answer
Therefore f and g are inverses of each other
Work Step by Step
$f(x) = \frac{x - 5}{3x + 4}$
Find the inverse
$y = \frac{x - 5}{3x + 4}$
y(3x + 4) = x - 5
3xy + 4y = x - 5
4y + 5 = x - 3xy
4y + 5 = x(1 - 3y)
$\frac{4y + 5}{1 - 3y} = x$
$f^{-1}(x) = \frac{4x + 5}{1 - 3x}$ = g(x)
$g(x) = \frac{5 + 4x}{1 - 3x}$
Find the inverse
$y = \frac{5 + 4x}{1 - 3x}$
y(1 - 3x) = 5 + 4x
y - 3xy = 5 + 4x
y - 5 = 4x + 3xy
y - 5 = x(4 + 3y)
$\frac{y - 5}{4 + 3y} = x$
$g^{-1}(x) = \frac{x - 5}{4 + 3x}$ = f(x)
Therefore f and g are inverses of each other
