GIven the function f(x) = 3x +1: (A) Find the inverse of f^-1(x). (B) Find f^-1(6)

1 answer:

3 0

The inverse function is equal to f-1(x) = (x - 1)/3 and the value at f-1(6) is equal to 5/3.

To find the inverse, you need to switch the f(x) and x in the equation. Then you can solve for the new f(x). The result will be the inverse (f-1)

f(x) = 3x + 1 ----> Switch f(x) and x

x = 3f(x) + 1 ----> Subtract 1

x - 1 = 3f(x) ----> Divide by 3.

f-1(x) = (x - 1)/3

Now that we have the inverse, we can plug 6 in to get the value at f-1(6).

f-1(x) = (x - 1)/3

f-1(6) = (6 - 1)/3

f-1(6) = 5/3

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uranmaximum [27]

Answer:

The airplane flies 95 miles.

Step-by-step explanation:

First we need to find the distance for the first segment using the formula for distance $D=\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}$ . Let's say $(x_{1},y_{1})$ is (0, 0) and $(x_{2},y_{2})$ is (33, 56). This gets us that the length of this segment is 65 miles.
Next, we need to find the distance for the second segment. Using the same formula for distance $D=\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}$ , we can say $(x_{1},y_{1})$ is now (33, 56) and $(x_{2},y_{2})$ is now (23, 32). This gets us that the length of this segment is 26 miles.
To get the total distance traveled, add the length of these two segments together (65 miles + 26 miles) to get 91 total miles traveled.