Answer
a) Find the inverse equation
$f^{-1}(x) = \frac{x-3}{2}$
b) Verify that the inverse equation is correct
$f(f^{-1}(x)) = x$
$f(\frac{x-3}{2}) = 2(\frac{x-3}{2}) + 3$
$= \frac{2(x-3)}{2} + 3$
$= x - 3 + 3$
$= x$
$f^{-1}(f(x)) = x$
$f^{-1}(2x + 3) = \frac{(2x+3) -3}{2}$
$= \frac{2x + 3 - 3}{2}$
$= \frac{2x}{2}$
$= x$
Therefore, the inverse equation is correct.
Work Step by Step
a) Find the inverse function
Let $f(x) = y$
$y = 2x + 3$
$x = 2y + 3$
$x - 3 = 2y$
$y = \frac{x-3}{2}$
$f^{-1}(x) = \frac{x-3}{2}$
b) Verify that the inverse equation is correct
$f(f^{-1}(x)) = x$
$f(\frac{x-3}{2}) = 2(\frac{x-3}{2}) + 3$
$= \frac{2(x-3)}{2} + 3$
$= x - 3 + 3$
$= x$
$f^{-1}(f(x)) = x$
$f^{-1}(2x + 3) = \frac{(2x+3) -3}{2}$
$= \frac{2x + 3 - 3}{2}$
$= \frac{2x}{2}$
$= x$
Therefore, the inverse equation is correct.
