1. Evaluate the function f(x)=3x-1 using the domain of -2, 0, 3, and 5. Results are to be shown in a table.

2. Determine the domain of the inverse of the function given in problem 2. Explain the reasoning.

The inverse function [tex]f^{-1}(x)[/tex] has the domain which is the range of the function f(x) (all possible values of f(x)), so the domain of inverse function is {-7,-1,8,14}

eudora eudora · Answer 2 · 2019-09-03T17:04:18+02:00

Answer:

Step-by-step explanation:

1) . The given function is f(x) = 3x - 1

Using the domain or value of x = -2, 0, 3, and 5 we have to formulate a table for the value of the function.

f(-2) = 3(-2) - 1

= -7

f(0) = 3×0 - 1

= -1

f(3) = 3(3) - 1

= 9 - 1

= 8

f(5) = 3(5) - 1

= 15 - 1

= 14

x -2 0 3 5

y -7 -1 8 14

2). Since f(x) = 3x - 1

Now we can rewrite the function in the form of an equation.

y = 3x - 1

To formulate the inverse of the given function we will flip x by y.

x = 3y - 1

then we will solve it for the value of y.

3y = x + 1

y = [tex]\frac{1}{3}(x + 1)[/tex]

Or [tex]f^{-1}(x)=\frac{1}{3}(x+1)[/tex]

Now this inverse function will be defined for all real numbers.

Therefore, domain of [tex]f^{-1}(x)[/tex] will be all real numbers.

1. Evaluate the function f(x)=3x-1 using the domain of -2, 0, 3, and 5. Results are to be shown in a table. 2. Determine the domain of the inverse of the function given in problem 2. Explain the reasoning.

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1. Evaluate the function f(x)=3x-1 using the domain of -2, 0, 3, and 5. Results are to be shown in a table.

2. Determine the domain of the inverse of the function given in problem 2. Explain the reasoning.