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Vera_Pavlovna [14]
2 years ago
5

PLEASE HELP ME SOLVE THIS

Mathematics
1 answer:
yan [13]2 years ago
8 0
One to one means only one x value gives one y value

This only happens when x is greater than or equal to -1 [-1, infinity) or when x is less than or equal to -1 (-infinity, -1].

Non decreasing means the slope is zero or positive, so it has to be the first option for the domain [-1, infinity]

The inverse of f(x) = (x + 1)^2
y = (x + 1)^2
x = (y + 1)^2
Sq rt x = y + 1
(sq rt x) - 1 = y
f^-1(x) = (sq rt x) - 1

We cannot take the square root of -1, so the domain of the inverse of f is [0, infinity]
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Answer:

Point-slope form of equation given as $y-2=-2(x+2)$.

Slope-intercept form of equation is given as $y=-2 x-2$.

Step-by-step explanation:

In the question, it is given that the slope of a line is -2 and it passes from (-2,2).

It is asked to write the point-slope form of the equation and rewrite it as slope-intercept form.

To do so, first find the values which are given in the question and put it in the formula of point-slope form. Simplify the equation to rewrite as slope-intercept form.

Step 1 of 2

Passing point of the line is (-2,2).

Hence, $x_{1}=-2$ and

$$y_{1}=2 \text {. }$$

Also, the slope of the line is -2.

Hence, m=-2

Substitute the above values in point-slope form of equation given by $y-y_{1}=m\left(x-x_{1}\right)$

$$\begin{aligned}&y-y_{1}=m\left(x-x_{1}\right) \\&y-2=-2(x-(-2) \\&y-2=-2(x+2)\end{aligned}$$

Hence, point-slope form of equation given as y-2=-2(x+2).

Step 2 of 2

Solve y-2=-2(x+2) to write it as slope-intercept form given by y=mx+c.

$$\begin{aligned}&y-2=-2(x+2) \\&y-2=-2 x-4 \\&y=-2 x-4+2 \\&y=-2 x-2\end{aligned}$$

Hence, slope-intercept form of equation is given as y=-2x-2.

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