Given f(x) = (-1/7)(sqrt 16-x^2), find f^-1(x). then state whether the inverse is a function.

Step-by-step explanation:

The usual method of finding the inverse of a function is to solve for y the equation ...

  x = f(y)

The inverse is only defined on the range of the original function, so for ...

  0 ≥ x ≥ -4/7

Here, that looks like ...

  x = (-1/7)√(16 -y^2)

  -7x = √(16 -y^2) . . . multiply by -7

  49x^2 = 16 -y^2 . . . square both sides

  y^2 + 49x^2 = 16 . . . add y^2

  y^2 = 16 -49x^2 . . . . subtract 49x^2

  y = ±√(16 -49x^2) . . . . take the square root

So, the inverse function is ...

  f^-1(x) = ±√(16 -49x^2) . . . . . defined only for -4/7 ≤ x ≤ 0

This gives two output values for each input value, so is not a function.

The original f(x) is the bottom half of an ellipse, so does not pass the horizontal line test. It cannot have an inverse function.

the correct answer is b. negative exponential growth.

step-by-step explanation:

you can tell it's an exponential function because it decreases rapidly then levels out and never touches the x-axis.

it is negative because the y-axis decreases as the x-axis increases.

therefore it is a negative exponential growth graph.

hope i !

the argument of alfred t. mahan, henry cabot lodge, and albert j. beveridge was the economically and mass production the the americans could not consume themselves. this led expansion to sell to other foreign nations for profits.

step-by-step explanation:

this is my explanation