Inverse Function – MATHEMATICS

by | Sep 12, 2022 | Uncategorized

a. Write an equation for the inverse function in the form of y=f^-1(x), b. graph f and f^-1 on the axes, and c. give the domain and the range of f and f^-1. If the function is not one-to-one, say so.1. y=4x-52. y=4/xa. Write an equation for the inverse function in the form of y=f^-1(x), b. graph f and f^-1 on the axes, and c. give the domain and the range of f and f^-1. If the function is not one-to-one, say so. 1. y=4x-5
Inverse function
y = 4x – 5
Change x as y and y as x,
x = 4y – 5
Write the y as function of x.
4y = x + 5
y = (x + 5)/4
f^-1(x) = (x + 5)/4GraphDomain and Range
y = 4x – 5
Domain: Set of all real numbers
Range: Set of all real numbers
f^-1(x) = (x + 5)/4
Domain: Set of all real numbers
Range: Set of all real numbersBoth the functions are linear, so they are one-to-one function.2. y=4/x
Inverse function
Change x as y and y as x,
x = 4/y
Write the y as function of x.
y = 4/x
f^-1(x) =4/x
Both the f and f^(-1) are the same.
GraphDomain and Range
The function 4/x is not defined at x = 0.So domain: Set of all real numbers except zero
Range: Set of all real numbers
The function is one-to-one function.



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