Inverse Basics
The first step in finding the inverse is...
Replace f(x) with y
The inverse of this function is...
f(x) = 25 /
x + 1
f^-1(x) = 25 /
(x - 1)
The two functions are inverses of each other if...
After completing the composition, both functions end up equalling x
There are ____ seasons in Grey’s Anatomy...
17
When the inverse is found, instead of writing it as y = (inverse) it is written as...
f^-1(x) = (inverse)
The inverse of this function is...
f(x) = (7x + 11) /
(3 + x)
f^-1(x) = (3x - 11) /
(7 - x)
You set up a composition problem by...
Plug one function into the other function for every x that is in the function
ex. f(x) will be plugged into every x in the function g(x) and vice versa
Taylor Swift has ____ albums...
9
An inverse is...
The reverse (opposite) function of the original function
ex. f(x) = x - 2 --> f^-1(x) = x + 2
The domain and range of the inverse of this function is...
f(x) = (5x+2) /
(x-3)
D: ℝ, x ≠ 5
R: ℝ, y ≠ 3
When working with rationals, having a fraction over another fraction can be avoided in a composition problem by...
Multiplying each term in the numerator and the denominator by the common denominator of both fractions
The richest city in the world in 2021 is...
Qatar
You manipulate a function to find it's inverse by...
Switching the x's and y's in the function
Evaluating the inverse of this function, at x = 4.14, will be...
f(x) = (4x - 7) /
(x - 2)
9.14
The f(g(x)) function for the composition problem would be set up as...
f(x) = (2 - 4x) / g(x) = (2x + 2) /
(3x - 1) (x - 1)
f(g(x)) = (2 - 4{(2x + 2)/(x-1)}) /
(3{(2x + 2)/(x-1)} - 1)
The song Beauty and the Beat by Justin Bieber ft. Nicki Minaj came out in the year...
2012
The domain and range of the original and inverse functions are found by...
The domain of the original will be the same as the range of the inverse. The range of the inverse is the same as the domain of the original.
The inverse of this function and the domain and range of both the original function and inverse function are...
f(x) = (3x + 10) /
(2x + 5)
Inverse: f^-1(x) = (-5x + 10) / (2x - 3)
Domain and Range (original):
D: ℝ, x ≠ -5/2 R: ℝ, y ≠ 3/2
Domain and Range (inverse):
D: ℝ, x ≠ 3/2 R: ℝ, y ≠ -5/2
The following two functions are....
f(x) = (2x + 1) / g(x) = (-4x + 1) /
(3x + 4) (3x - 2)
inverses!
The #1 rated college in the U.S. is...
Harvard University