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4 years ago

9. What is the domain and range for the following function and its inverse? F(x)=x^2+3

2 answers:

mote1985 [20]4 years ago

4 0

F(x)=x^2+3 has a domain of X> or equal to 3, and a range of all real numbers
I'm not too sure about the inverse but I think the equation is
sqrt(x-3)=y

diamong [38]4 years ago

4 0

The domain is the kind of numbers that can be put into the function.

The range is the kind of numbers that result from solving the function.

f(x) = x² + 3.

Any real number, positive or negative can be substituted into the function.

But when the function is carried, out because of the x² , the result would come out as positive number greater than zero.

Therefore the domain of f(x) is any Real number, R

The range, is a set of Real numbers greater than zero. R > 0

Hope this helps.

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assume x and y are both differentiable functions of t. find dx/dt given x=-1 and dy/dt=8 for the relation: 4x^2+3y^3=28

melomori [17]

Given:

x and y are both differentiable functions of t.

$4x^2+3y^3=28$

$x=-1\text{ and }\dfrac{dy}{dt}=8$

To find:

The value of $\dfrac{dx}{dt}$ .

Solution:

We have,

$4x^2+3y^3=28$ ...(i)

At x=-1,

$4(-1)^2+3y^3=28$

$4+3y^3=28$

$3y^3=28-4$

$3y^3=24$

Divide both sides by 3.

$y^3=8$

Taking cube root on both sides.

$y=2$

So, y=2 at x=-1.

Differentiate (i) with respect to t.

$4(2x\dfrac{dx}{dt})+3(3y^2\dfrac{dy}{dt})=0$

Putting x=-1, y=2 and $\dfrac{dy}{dt}=8$ , we get

$4(2(-1)\dfrac{dx}{dt})+3(3(2)^28)=0$

$-8\dfrac{dx}{dt}+9(4)(8)=0$

$-8(\dfrac{dx}{dt}-9(4))=0$

Divide both sides by -8.

$\dfrac{dx}{dt}-36=0$

$\dfrac{dx}{dt}=36$

Therefore, the value of $4x^2+3y^3=28$ is 36.

6 0

3 years ago

No link or bot answer the question

Oduvanchick [21]

Answer:

5^11

Step-by-step explanation:

5^7/5^-7 is basically 5^7x5^7 which is 5^14. 5^14x5^-3 is 5^11.

7 0

2 years ago

Read 2 more answers

Find the value of y required for

Ulleksa [173]

This is algebra disguised as geometry. I object. There are much better ways to combine algebra and geometry.

Anyway, in a parallelogram the diagonals meet at their midpoints, so bisect each other. So we have two pairs of congruent segments; geometry over.

3x + 1 = x+27

79 - y = 2y + 22

We can ignore the one about x.

79 - 22 = 2y + y

57 = 3y

y = 19

Answer: 19

6 0

3 years ago

Does the picture below indicate that JAC DBE

Over [174]

Answer:

Step-by-step explanation:

The box in angle b means that it is a right angle and right angles are 90 degrees

The angle marked A is 93 degrees

The angles are not equal

6 0

3 years ago

Solve triangle ABC given that A = 56°, B = 57°, and b = 9.00. Round the length of the sides to the nearest hundredth

daser333 [38]

Answer:

Part 1) $C=67^o$

Part 2) $a=8.90\ units$

Part 3) $c=9.88\ units$

Step-by-step explanation:

step 1

Find the measure of angle C

Remember that the sum of the interior angles of any triangle must be equal to 180 degrees

$A+B+C=180^o$

substitute the given values

$56^o+57^o+C=180^o$

$C=180^o-113^o=67^o$

step 2

Find the length side a

Applying the law of sines

$\frac{a}{sin(A)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{a}{sin(56^o)}=\frac{9.00}{sin(57^o)}$

solve for a

$a=\frac{9.00}{sin(57^o)}sin(56^o)$

$a=8.90\ units$

step 3

Find the length side c

Applying the law of sines

$\frac{c}{sin(C)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{c}{sin(67^o)}=\frac{9.00}{sin(57^o)}$

solve for c

$c=\frac{9.00}{sin(57^o)}sin(67^o)$

$c=9.88\ units$

3 0

4 years ago