This is calculation based question. Here, we calculate the value of a= 2, b=1 and c= -2.
Given:
[tex]f(x)= log_0_._5x[/tex] and its inverse is [tex]f^{-1} (x) = 0.5^{x}[/tex] .
We need to determined the value of a, b and c for the inverse function.
Therefore, firstly we substitute the value of x= -1 in given inverse function and calculate the value of a.
So,
[tex]f^{-1} (x) = 0.5^{x}\\\\f^{-1} (-1) = (0.5)^{-1}\\\\f^{-1} (-1) = 2[/tex]
Thus, the value of a is 2.
Now calculate the value of b, by substitute the value of x is 0 in given inverse function.
We get,
[tex]f^{-1} (x) = 0.5^{x}\\\\f^{-1} (0) = (0.5)^{0}\\\\f^{-1} (0) = 1[/tex]
And, calculate the value of c, by substitute the value of x is 2 in given inverse function.
We get,
[tex]f^{-1} (x) = 0.5^{x}\\\\f^{-1} (2) = (0.5)^{2}\\\\f^{-1} (2) = -2[/tex]
Therefore, the value of a= 2, b=1 and c=-2.
For more details, please refer this link:
https://brainly.com/question/15912209
