please help!...I'm on the verge of failing!!!!!!?

Question

how do you find the inverse of...
y=2x+1, and how do you graph that...
how do you graph y=x
how do you find the inverse of y=x
....and graph that...

Answer 1

To find the inverse of y = 2x+1, follow this recipe:
1. Interchange x and y.
x = 2y+1
2. Solve it for y:
y = (x-1)/2
3. Check: 2(x-1)/2 + 1 = x, so done.
Now graph y = (x-1)/2.

For the second problem, if we follow this recipe,
We find that the inverse of y = x is also y = x.
In other words, this function is its own inverse.

Answer 2

To find the inverse of the line, switch the places of the x and y. Then to graph the equation you might have to solve for y. Your example would be y=x/2 -1/2. The equation y=x is a line that has a slope of 1 and goes through the origin. If it helps it goes through the points (1,1), (2,2), (3,3), etc. The inverse of this line is the same line.

Answer 3

let f(x) = y = 2x + 1,
let z = f^(-1) (x) be inverse of f(x),
then x = f(z) = 2z + 1,
z = (1/2)x - (1/2),
inverse of y = 2x + 1 is y = (1/2)x - (1/2),
x = 0 ==> y = -1/2,
y = 0 ==> (1/2)x - (1/2) = 0 ==> x = 1,
graph is line thru x-int = 1 & y-int = -1/2.

y = x,
x = 0 ==> y = 0,
x = 1 ==> y = 1,
graph is line thru origin & point (1, 1).

inverse of y = x is y = x itself (memorize it),
graph: discussed above.

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