SOLUTION: is 1 + sqrt(-x-2) a one-to-one function?

Question 1146776: is 1 + sqrt(-x-2) a one-to-one function?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe so.
the test is that, for every value of x, there is only one value of y, and for every value of y, there is only one value of x.

to make that expression a function, let y = that expression.

you get y = 1 + sqrt(-x-2)

since the expression under the squqare root sing has to be >= 0, you get:

-x-2 >= 0
add 2 to both sides to get:
-x >= 2
multiply both sides by -1 to get:
x <= -2

note that, when you multiply both sides of an inequality by a negative number, the inequality reverses.

the domain of the function is therefore all real values of x <= -2.

the function is, once again, y = 1 + sqrt(-x-2)
when x = -2, y = 1 + sqrt(2 - 2) = 1 + sqrt(0) = 1 + 0 = 1.
when x = -6, y = 1 + sqrt(6 - 2) = 1 + sqrt(4) = 1 + 2 = 3.
whwn x = -27, y = 1 + sqrt(27 - 2) = 1 + sqrt(25) = 1 + 5 = 6.

the greaph of the equation of y = 1 + sqrt(-x-2) is shown below.

$$$

the function passes the vertical line test and the horizontal line test.
here's a reference.
https://www.dummies.com/education/math/algebra/identify-one-to-one-functions-using-vertical-and-horizontal-line-tests/

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