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Yuki888 [10]
4 years ago
15

If f(x) and its inverse function,f-1(x), are both plotted on the same coordinate plane, where is their point of intersection?

Mathematics
2 answers:
cluponka [151]4 years ago
4 0

Answer:

C. (2, 2)

Step-by-step explanation:

this is the correct answer on ed-genuity, hope this helps! :)

Mice21 [21]4 years ago
3 0
Consider f, such that f(x)=y, where x is in the Domain of f, and y is in the Range of f.

Let f(a)=b. So, (a, b) is in the graph of f.


The inverse function of f, f^{-1} (if exists) is such that  if f(x)=y, then f^{-1}(y)=x.

So if (a, b) is a particular point in the graph of f, then (b, a) is a point in the graph of  f^{-1}.

 
A point where they intersect is a point where (a, b)=(b, a), that is a=b. Among our choices, only (2, 2) satisfies this condition.


Answer: (2, 2)
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a rectangular box with two sqaure opposite ends is to hold 8000 cubic inches. find the dimensions of the cheapest box if tge rec
AveGali [126]

Answer:

the dimensions of the box that minimizes the cost are 5 in x 40 in x 40 in

Step-by-step explanation:

since the box has a volume V

V= x*y*z = b=8000 in³

since y=z (square face)

V= x*y² = b=8000 in³

and the cost function is

cost = cost of the square faces *  area of square faces + cost of top and bottom * top and bottom areas + cost of the rectangular sides * area of the rectangular sides

C = a* 2*y² +  a* 2*x*y + 15*a* 2*x*y =  2*a* y² +  32*a*x*y

to find the optimum we can use Lagrange multipliers , then we have 3  simultaneous equations:

x*y*z = b

Cx - λ*Vx = 0 → 32*a*y -  λ*y² = 0 → y*( 32*a-λ*y) = 0 → y=32*a/λ

Cy - λ*Vy = 0  → (4*a*y + 32*a*x) - λ*2*x*y = 0

4*a*32/λ  + 32*a*x - λ*2*x*32*a/λ = 0

128*a² /λ +  32*a*x - 64*a*x = 0

32*a*x = 128*a² /λ

x  = 4*a/λ

x*y² = b

4*a/λ * (32*a/λ)² = b

(a/λ)³ *4096 =  8000 m³

(a/λ) = ∛ ( 8000 m³/4096 ) = 5/4 in

then

x  = 4*a/λ = 4*5/4 in = 5 in

y=32*a/λ = 32*5/4 in = 40 in

then the box has dimensions 5 in x 40 in x 40 in

3 0
4 years ago
Determine which postulate or theorem can be used to prove that ABC=DCB.
butalik [34]

Answer:

A. SAS

Step-by-step explanation:

In the figure attached, the triangles are shown.

The Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

In this case, the two sides of triangle ABC are AC and BC and the included angle is ∠C, which are congruent with sides BD and BC and the included angle ∠B from triangle BCD

5 0
4 years ago
Read 2 more answers
if alpha and beta are the roots of the equation 2 x square - 7 x - 3 is equal to 0 find alpha + beta​
Lorico [155]

Answer:

Values for alpha and beta are 0.5 and 3.

Step-by-step explanation:

2x² - 7x - 3 = 0

2x² - 7x - 3 = (2x - 1 )(x - 3)

∴ (2x - 1 )(x - 3) = 0

The only way to get zero by multiplying two values together, is if one of those values is qual to zero. Therefore, either (2x - 1 )=0, or (x - 3)=0.

If (2x - 1 )=0

∴2x=1

∴x=0.5

If (x - 3)=0

∴x=3

We have two values for x. These values represent alpha and beta.

<em>(BTW - I'm not sure from the phrasing of your question whether or not you just want to find the values or whether you want to find the sum of the values (I don't know if you used '+' to mean 'and' or 'plus'), but if you do want to find the sum, it's of course just 0.5+3= 3.5.)</em>

8 0
3 years ago
4x+3y=47.50<br> 7x+1y=47.00<br> How do you do the substitution?
Makovka662 [10]
Well, the only thing you have to do is use like terms. As you can see, you have 4x and 7x. These two are like terms because they both have the same variable. Just like 3y and 1y. 
3 0
4 years ago
My question is y = 4x + 1 and my options are<br>a. 4, 3 <br>b. 4,1<br>c. 1,4<br>d. 3,1​
Akimi4 [234]

Answer:

B. 4,1

Step-by-step explanation:

7 0
4 years ago
Read 2 more answers
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