The ordered pair on the inverse of f(x) = (-1, -2)
The range of the inverse of f(x) = {-8, -4, 0, 4, 8}
The table representing the relationship between x and f(x) is attached as a diagram to this solution
By carefully observing the table shown, the relationship between x and f(x) is:
f(x) = x/2
To find the inverse of f(x), first make x as the subject of the formula:
x = 2f(x)
Replace x by f^-1(x), and f(x) by x:
[tex]f^{-1} (x) = 2x[/tex]
When x = -1:
[tex]f^{-1} (x) = 2(-1)\\f^{-1} (x) = -2[/tex]
Therefore, the ordered pair that is on the inverse of f(x) is (-1, -2)
To find the range of inverse of f(x), find the values of f^-1(x) for the given values of x:
For x = -4, f^-1(x) = 2(-4) = -8
For x = -2, f^-1(x) = 2(-2) = -4
For x = 0, f^-1(x) = 2(0) = 0
For x = 2, f^-1(x) = 2(2) = 4
For x = 4, f^-1(x) = 2(4) = 8
The range of the inverse of f(x) for the given values of x is given as:
Range = {-8, -4, 0, 4, 8}
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