# Inverse Function

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-5

2. y=4/x

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

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-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)/4

Graph

Domain 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 numbers

Both 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.

Graph

Domain 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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