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Naya [18.7K]
3 years ago
5

What is the domain of the function f(x)=square root of 2-x?

Mathematics
1 answer:
SVEN [57.7K]3 years ago
5 0

Answer:

domain : ] -∞ , 2]

Step-by-step explanation:

the value of 2-x must be more than or equal to 0

because you there is no square root for negative number

2-x ≥ 0

x ≤ 2

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What is the equation for the line that contains the points (-5 , 2) and (3 , 7)?
baherus [9]

Answer:

y=\frac{5}{8} x+\frac{41}{8}

Step-by-step explanation:

Hope this helps!

5 0
3 years ago
Calculus piecewise function. ​
Kipish [7]

Part A

The notation \lim_{x \to 2^{+}}f(x) means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.

So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc

We don't actually arrive at x = 2 itself. We simply move closer and closer.

Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2

Therefore f(x) = (x/2) + 1

Plug in x = 2 to find that...

f(x) = (x/2) + 1

f(2) = (2/2) + 1

f(2) = 2

This shows \lim_{x \to 2^{+}}f(x) = 2

Then for the left hand limit \lim_{x \to 2^{-}}f(x), we'll involve x < 2 and we go for the first piece. So,

f(x) = 3-x

f(2) = 3-2

f(2) = 1

Therefore, \lim_{x \to 2^{-}}f(x) = 1

===============================================================

Part B

Because \lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x) this means that the limit \lim_{x \to 2}f(x) does not exist.

If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.

===============================================================

Part C

You'll follow the same type of steps shown in part A.

However, keep in mind that x = 4 is above x = 2, so we'll deal with x > 2 only.

So you'd only involve the second piece f(x) = (x/2) + 1

You should find that f(4) = 3, and that both left and right hand limits equal this value. The left and right hand limits approach the same y value. The limit does exist here. There are no gaps to worry about when x = 4.

===============================================================

Part D

As mentioned earlier, since \lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3, this means the limit \lim_{x \to 4}f(x) does exist and it's equal to 3.

As x gets closer and closer to 4, the y values are approaching 3. This applies to both directions.

4 0
1 year ago
How do I solve this problem −24−18p=38p?
Leni [432]
P would equal -3/7
Hope it helps!

5 0
3 years ago
Read 2 more answers
Jose’s school has 426 students. His principal has promised the Student Council that their idea will be carried out if they can g
Kryger [21]

Answer: Step 4

<u>Step-by-step explanation:</u>

1. Define variable x as student signatures still needed  (Correct)

2)\ \dfrac{x+82}{426}              (Correct)

3. 25% = 0.25      (Correct)

4)\ \dfrac{x+82}{426}\leq 0.25      (Error)!

The inequality symbol should be GREATER THAN or equal to (≥) because Jose needs 25% or more (not less).

6 0
3 years ago
Read 2 more answers
A car traveled 360 miles in 4 hours. If its speed were to be 15 mph slower, how long would it take to travel the same distance?
docker41 [41]

Answer:

4.8 hours

Step-by-step explanation:

First, divide the distance by time to get velocity.

S = D/T

S = 360/4

S = 90 mph

Then, subtract 15 from 90 to get the new speed.

90 - 15 = 75

Lastly divide the distance by the new speed to get time.

T = D/S

T = 360/75

T = 4.8

Therefore, it would take the car 4.8 hours to travel 360 miles at 75 miles per hour.

6 0
3 years ago
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