Question

find the inverse function of the function $f(x) = 2x + 3$.
answer
$\bigcirc$ $f^{-1}(x) = \frac{1}{2}x - 3$
$\bigcirc$ $f^{-1}(x) = 2x - 3$
$\bigcirc$ $f^{-1}(x) = \frac{x-3}{2}$
$\bigcirc$ $f^{-1}(x) = \frac{x+3}{2}$
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Explanation:

Step1: Replace $f(x)$ with $y$

$y = 2x + 3$

Step2: Swap $x$ and $y$

$x = 2y + 3$

Step3: Isolate $2y$

$2y = x - 3$

Step4: Solve for $y$

$y = \frac{x-3}{2}$

Step5: Replace $y$ with $f^{-1}(x)$

$f^{-1}(x) = \frac{x-3}{2}$

Answer:

$f^{-1}(x) = \frac{x-3}{2}$