Answer: [tex]f^-1(1)=-1[/tex]
Step-by-step explanation:
From the graph given we can derive the function [tex]f(x)[/tex]
[tex]f(x) = .5x + 1.5[/tex]
To solve [tex]f^-1(1)[/tex] we need to find the inverse function of [tex]f(x)[/tex].
Inverse functions are functions that essentially "reverse" the mapping of the domain ([tex]x[/tex]) and range ([tex]y[/tex]) of the parent function.
To find the inverse function [tex]f(x)[/tex] we need to solve for x in terms of y.
[tex]y = .5x + 1.5[/tex]
[tex]y - 1.5 = .5x[/tex]
[tex]\frac{y - 1.5}{.5} = \frac{.5x}{.5}[/tex]
[tex]x=2y-3[/tex]
from this, we can derive that
[tex]f(y)^-1=2y-3[/tex]
this can also be written as a function of x
[tex]f(x)^-1 = 2x-3[/tex]
both functions are identical.
take one of these functions and you can find that
[tex]f^-1(1) = 2(1) - 3[/tex]
[tex]f^-1(1) = -1[/tex]
