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# Inverse Function

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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.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

© BrainMass Inc. brainmass.com October 5, 2022, 1:09 am ad1c9bdddf>
https://brainmass.com/math/algebra/inverse-function-451257