If <img src="https://tex.z-dn.net/?f=t_n" id="TexFormula1" title="t_n" alt="t_n" align="absmiddle" class="latex-formula"> = 11n−

What are the domain and range of f(x)-[x-2] +1

svetlana [45]

Replace f(x)f(x) with yy.y=x2−1y=x2-1

Interchange the variables.x=y2−1x=y2-1

Solve for yy.
y=√1+x,−√1+xy=1+x,-1+x

Solve for yy and replace with f−1(x)f-1(x).
This is your answer=f−1(x)=√1+x,−√1+xf-1(x)=1+x,-1+x
Hope you have a wonderful day! hope this helps!

7 0

3 years ago

ABCD is a rectangle. The measure of angle BCE is 4x-23 and the angle measure of angle DCE is 5+5x. Find the measure of angle BEC

Temka [501]

<h2>Explanation:</h2><h2></h2>

The diagram for this problem is shown below. Point E is the intersection of the two diagonals and we know that:

$\angle BCE=\beta \\ \\ \angle DCE=\theta$

Every internal angle of any rectangle measures 90 degrees, so:

$\beta +\alpha=90 \\ \\ (4x-23)+(5+5x)=90 \\ \\ \\ Isolating \ x: \\ \\ (4x+5x)+(5-23)=90 \\ \\ 9x-18=90 \\ \\ 9x=108 \\ \\ x=\frac{108}{9}=12$

So:

$\beta=4x-23=4(12)-23=25^{\circ}$

So the measure of angle BEC can be found as follows:

We know that triangle ΔCEB is an isosceles triangle because the diagonals of any rectangle measure the same. So

$\angle EBC=\beta$

The sum of internal angles of any triangle add up to 180 degrees, so:

$\beta + \beta+\angle BEC=180^{\circ} \\ \\ 2\beta+\angle BEC=180^{\circ} \\ \\ \angle BEC=180^{\circ}-2\beta \\ \\ \angle BEC=180^{\circ}-2(25^{\circ}) \\ \\ \angle BEC=180^{\circ}-50^{\circ} \\ \\ \boxed{\angle BEC=130^{\circ}}}$

7 0

4 years ago

Can someone tell me what the blue lines mean?

Radda [10]

Answer:

It means the two lines are equal in length.

7 0

3 years ago

Read 2 more answers

What is the value of x if Y=log x & If y=10?

jok3333 [9.3K]

Answer:

x = $10^{10}$

I'm not great at explaining answers like this. Please ask a teacher etc. for a better explanation!

Hope this helps and have a nice day!

7 0

3 years ago

A fence must be built to enclose a rectangular area of 20,000 ft^2. Fencing material costs $4 per foot for the two sides facing

Marysya12 [62]

The cost of the least expensive fence is $3200

Step-by-step explanation:

The given is:

A fence must be built to enclose a rectangular area of 20,000 ft²
Fencing material costs $4 per foot for the two sides facing north and south and $8 per foot for the other two sides

We need to find the cost of the least expensive fence

Assume that the length of each side opposite to North or South is x feet and the length of each other sides is y feet

∵ The length of the rectangle = x feet

∵ The width of the rectangle = y feet

∵ The rectangular area is 20,000 ft²

- Area of a rectangle = length × width

∴ x × y = 20,000

- Divide both sides by x to find y in terms of x

∴ $y=\frac{20,000}{x}$