SOLUTION: 3.26 For the function f(x)=4x-5 determine whether f(x) is one-to-one. If so, find a formula for the inverse, give the domain and range for f^-1 , and then graph both functions

Question 1012558: 3.26
For the function f(x)=4x-5 determine whether f(x) is one-to-one. If so, find a formula for the inverse,
give the domain and range for f^-1 , and then graph both functions on the same axes.
1. Is f(x) a one-to-one function? Yes or No
2. The inverse function is f^-1 =
3. What is the correct range?
4.Graph for f and f^-1A:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
For the function f(x)=4x-5 determine whether f(x) is one-to-one. If so, find a formula for the inverse,
give the domain and range for f^-1 , and then graph both functions on the same axes.
1. Is f(x) a one-to-one function? Yes or No
yes - it's an equation for a straight line which is always 1 to 1.

2. The inverse function is f^-1 =

set f(x) = y and the function becomes y = 4x-5

the inverse function is x = 4y - 5

it is found by replacing y with x and x with y.

you can solve this function for y in the following manner:
start with x = 4y - 5
subtract x from both sides of the equation and subtract 4y from both sides of the equation to get -4y = -x - 5
divide both sides of the equation by -4 to get y = x/4 + 5/4

x = 4y - 5 and y = x/4 + 5/4 are identical equations.
they are both inverse equations of y = 4x - 5.

3. What is the correct range?

the domain of the original function is all real values of x.
the range of the original function is all real values of y.

the domain of the inverse equation is the same as the range of the original function.

the range of the inverse equation is the same as the domain of the original function.

4.Graph for f and f^-1A:

graph is shown below:

the original equation is red.
the inverse equation is blue.
both x = 4y-5 and y = 4x+5/4 are blue.
since these equations are identical, they show up as the same line on the graph.
the dashed line of y = x is also shown.
since the equations are inverses of each other, they are symmetric about the line y = x.
$$$

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