Question

1. the function f is given by $f(x) = 3log_2(x) + 8$. find $f^{-1}(x)$. $f(x)=3log_2(x)+8$ $y = 3log_2(x)+8$ $x = 3log_2(y)+8$

Explanation:

Step1: Set $y=f(x)$

$y = 3\log_{2}(x) + 8$

Step2: Swap $x$ and $y$

$x = 3\log_{2}(y) + 8$

Step3: Isolate the logarithm term

$x - 8 = 3\log_{2}(y)$
$\frac{x - 8}{3} = \log_{2}(y)$

Step4: Convert to exponential form

$y = 2^{\frac{x - 8}{3}}$

Answer:

$f^{-1}(x)=2^{\frac{x - 8}{3}}$