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2 years ago

Find f^-1(x) and it’s domain.

Mathematics

1 answer:

Mrac [35]2 years ago

7 0

Answer: A

Step-by-step explanation:

Letting $f(y)=x$ ,

$x=\sqrt{y}-5\\\\x+5=\sqrt{y}\\\\y=(x+5)^{2}$

Also, the domain of an inverse is the same as the range of the original function, so the range is $x \geq 0$

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A line segment has (x1, y1) as one endpoint and (xm, ym) as its midpoint. Find the other endpoint (x2, y2) of the line segment i

Tasya [4]

Answer:

(3,7) for the first line, and (12,0) for the second one.

Step-by-step explanation:

Hi Isabella,

1) The Midpoint of a line, when it comes to Analytical Geometry, is calculated as Mean of two points it follows:

$x_{m}=\frac{x_{1} +x_{2} } {2}, y_{m} =\frac{y_{1}+ y_{2} }{2}$

2) Each segment has two endpoints, and their midpoints, namely:

a) (1,-9) and its midpoint (2,-1)

b) (-2,18) and its midpoint (5,9)

3) Calculating. You need to be careful to not sum the wrong coordinates.

So be attentive!

The first line a

$2=\frac{1+x_{2} }{2}\\ 4=1+x_{2}\\ 4-1=-1+1+x_{2} \\ x_{2}=3\\-1=\frac{y_{2}-9}{2}\\-2=y_{2}-9\\+2-2=y_{2}-9+2\\ y_{2}=-7$

So (3,7) is the other endpoint whose segment starts at (1,-9)

The second line b endpoint at (-2,18) and its midpoint (5,9)

$5=\frac{-2+x_{2} }{2} \\ 10=-2+x_{2} \\ +2+10=+2-2+x_{2}\\ x_{2}=12 \\ \\ 9=\frac{18+y_{2} }{2} \\ 18=18+y_{2} \\ -18+18=-18+18+y_{2}\\ y_{2} =0$

So (12,0) it is the other endpoint.

Take a look at the graph below:

8 0

3 years ago

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3 years ago

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3 years ago