The answers are: [tex]F^{-1}[/tex](3) = -2
[tex](F^{-1} )^{1}[/tex](3) = -6
What is a function?
A function is an expression, equation or rule that defines a relationship between two or more variable.
Analysis:
Inverse of the function, f(x) = x-1/x+1
Let y = x-1/x+1
y(x+1) = x - 1
yx + y = x - 1
y +1 = x - yx
y+1 = x(1-y)
x = y+1/1-y
Inverse [tex]f^{-1}[/tex] = x+1/1-x
at x = 3
[tex]f^{-1}[/tex](3) = 3+1/1-3 = 4/-2 = -2
To find the derivative of x+1/1-x
u = x+1, du/dx = 1, v = 1-x, dv/dx = -1
derivative d[tex]f^{-1}[/tex](x)/dx = 1-x(1) -(x+1)(-1)/[tex](1-x)^{2}[/tex] = -2x/[tex](1-x)^{2}[/tex]
at x = 3
-2(3) / (1-3)2 = -6/4 = -3/2
Learn more about function: brainly.com/question/25638609
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