INVERSE
Today we defined the word “inverse”, were taught how to inverse a function and how to figure out if two given functions are the inverse of each other. Well, let’s get started…
Inverse: the set of ordered pairs obtained by interchanging the coordinates of each ordered pair in relation.
Example:
Original set of pairs --> [ ... (-3,3), (1,4), (4,5) ... ]
Inverse of set of pairs --> [ ... (3,-3), (4,1), (5,4) ... ]
* notice that all i did was switch the x and y values around in each pair
When graphing the original and inverse sets of pairs, each point must reflect the other across the y=x line on the graph. So, it will look like this:
Now, the next question is: How do you find the inverse of a function?
Well, according to Mrs. Ingram, if you follow these four steps, you'll be fine:
given function: f(x) = 3x - 2 find: f^-1(x)
STEP 1: Replace f(x) with y
y = 3x - 2
STEP 2: Interchange the x and y
x = 3y -2
STEP 3: Solve for y
x + 2 / 3 = y
STEP 4: Replace y with f^-1(x)
f^-1(x) = x+2 / 3
And there we have it. The inverse of the function f(x)=3x - 2 is f^-1(x)=x+2 / 3
But, what about if you are given: f(x)=3x-2 & m(x) =x+2 / 3 and it asks if those two functions are inverses of each other? To find out we must do the whole composition of functions thing ... lol. Here we go:
f(m(x)) & m(f(x))
f(x+2 / 3) = 3(x+2 / 3) - 2 ** the threes cancel out
= x + 2 - 2
= x
m(3x-2) = (3x-2) + 2 / 3
= 3x - 2 + 2 / 3
= 3x / 3
= x
Both compositions equal x which means the two functions are inverses of each other.
And... that's about it. We've come to the conclusion of the blog and let's make this quick. Next blogger shall be ... well remyshire asked for it so yeah.. it's her. Ex. 52 # 1-5,8,9,11 are the homework for tonight. And... well that's all folks. vamoose.
- cel
Well, according to Mrs. Ingram, if you follow these four steps, you'll be fine:
given function: f(x) = 3x - 2 find: f^-1(x)
STEP 1: Replace f(x) with y
y = 3x - 2
STEP 2: Interchange the x and y
x = 3y -2
STEP 3: Solve for y
x + 2 / 3 = y
STEP 4: Replace y with f^-1(x)
f^-1(x) = x+2 / 3
And there we have it. The inverse of the function f(x)=3x - 2 is f^-1(x)=x+2 / 3
But, what about if you are given: f(x)=3x-2 & m(x) =x+2 / 3 and it asks if those two functions are inverses of each other? To find out we must do the whole composition of functions thing ... lol. Here we go:
f(m(x)) & m(f(x))
f(x+2 / 3) = 3(x+2 / 3) - 2 ** the threes cancel out
= x + 2 - 2
= x
m(3x-2) = (3x-2) + 2 / 3
= 3x - 2 + 2 / 3
= 3x / 3
= x
Both compositions equal x which means the two functions are inverses of each other.
And... that's about it. We've come to the conclusion of the blog and let's make this quick. Next blogger shall be ... well remyshire asked for it so yeah.. it's her. Ex. 52 # 1-5,8,9,11 are the homework for tonight. And... well that's all folks. vamoose.
- cel
posted by Cel @ 11:06 PM
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