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20.08.2019 •
Mathematics
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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Ответ:
See explanation
Step-by-step explanation:
You are given the function![f(x)=3x-1](/tpl/images/0180/9530/b83a4.png)
The domain of the function are all possible values of variable x, so you can find f(x) for x=-2, 0, 3, 5:
The table is
The inverse function
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}
Ответ:
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 =![\frac{1}{3}(x + 1)](/tpl/images/0180/9530/c8fd6.png)
Or![f^{-1}(x)=\frac{1}{3}(x+1)](/tpl/images/0180/9530/ba3b9.png)
Now this inverse function will be defined for all real numbers.
Therefore, domain of
will be all real numbers.
Ответ: