Question

the inverse of the logarithmic function $f(x)=\log_{0.5}x$ is $f^{-1}(x)=0.5^{x}$.
what values of $a$, $b$, and $c$ complete the table for the inverse function?
$x$ $-2$ $-1$ $0$ $1$ $2$
$y$ $4$ $a$ $b$ $0.5$ $c$
$a = \square$ $b = \square$ $c = \square$

Explanation:

Step1: Substitute $x=-1$ into $f^{-1}(x)$

$a = 0.5^{-1} = \frac{1}{0.5} = 2$

Step2: Substitute $x=0$ into $f^{-1}(x)$

$b = 0.5^{0} = 1$

Step3: Substitute $x=2$ into $f^{-1}(x)$

$c = 0.5^{2} = \frac{1}{4} = 0.25$

Answer:

$a=2$, $b=1$, $c=0.25$