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pantera1 [17]
3 years ago
14

1. How do you determine whether a function is an inverse of another function?

Mathematics
1 answer:
-BARSIC- [3]3 years ago
8 0
<h3>Answer:</h3>
  1. Find the composite of the functions
  2. x/3
  3. All the answers are correct
  4. f(x) = 2+∛(x/3)
  5. f(x) = (x+3)/2
<h3>Step-by-step explanation:</h3>

1. If f(x) and g(x) are inverse functions, then f(g(x)) = g(f(x)) = x. Finding the composite of the two functions will tell you if they are inverses.

2. To find the inverse of a function, swap x and y, then solve for y.

... x = 3y

... x/3 = y . . . . . matches f(x) = x/3

3. A function will pass the vertical line test. If its inverse is also a function, that, too, will pass the vertical line test. Since the inverse of a function is that function reflected across y=x, any inverse function that passes the vertical line test corresponds to an original function that passes the horizontal line test. (A vertical line reflected across y=x is a horizontal line.)

4. See 2.

... x = 3(y -2)³

... (x/3) = (y -2)³ . . . . divide by 3

... ∛(x/3) = y -2 . . . . .take the cube root

... 2+∛(x/3) = y . . . . .add 2

... f(x) = 2+∛(x/3) . . . . is the inverse

5. See 2.

... x = 2y -3

... x+3 = 2y . . . . . add 3

... (x+3)/2 = y . . . .divide by 2

... f(x) = (x+3)/2 . . . .  is the inverse

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