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FrozenT [24]
3 years ago
15

For f(x)=√(2x+1) , find the following:

Mathematics
1 answer:
Wittaler [7]3 years ago
6 0

Part a.

The domain is the set of x values such that x \ge -\frac{1}{2}, basically x can be equal to -1/2 or it can be larger than -1/2. To get this answer, you solve 2x+1 \ge 0 for x (subtract 1 from both sides; then divide both sides by 2). I set 2x+1 larger or equal to 0 because we want to avoid the stuff under the square root to be negative.

If you want the domain in interval notation, then it would be \Big[ -\frac{1}{2} , \infty \Big) which means the interval starts at -1/2 (including -1/2) and then it stops at infinity. So technically it never stops and goes on forever to the right.

-----------------------

Part b.

I'm going to use "sqrt" as shorthand for "square root"

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

f(10) = sqrt(2*10+1) ... every x replaced by 10

f(10) = sqrt(20+1)

f(10) = sqrt(21)

f(10) = 4.58257569 which is approximate

-----------------------

Part c.

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

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

f(x+2a) = sqrt(2(x+2a)+1) ... every x replaced by (x+2a)

f(x+2a) = sqrt(2x+4a+1) .... distribute

we can't simplify any further

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Eddi Din [679]

Answer: 20% decrease.

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

Percent\ Change = \dfrac{New - Original}{Original}

\dfrac{32-40}{40} = \dfrac{-8}{40} =-0.20 = -20\%

The negative sign represents a decrease.

4 0
3 years ago
If f(x)=x-3/x and g(x) = 5x – 4, what is the domain of (f o g) (x)?
8_murik_8 [283]

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Step-by-step explanation:

7 0
3 years ago
Add lunch five friends share three pizzas equally what fraction of the pizza does each friend get
Hitman42 [59]

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5 0
3 years ago
A car travels 240 miles in 4 hours. at this rate, how many miles will it travel in 8 hours
oksian1 [2.3K]
First you need to find the rate. This problem is based on the formula d = rt
d = distance
r = rate 
t = time.

The question is asking how many miles will it travel in 8 hours so to find this out we need to find the rate when the car travels 240 miles in 4 hours. We use this information and plug it into the model d = rt

d = 240
r = don't know yet
t = 4 hr
d = rt 
240 = 4r
240 / 4 = 4r / 4
60 = r
r = 60
So the car is going at a rate of 60 miles per hour. Now that we know this we can solve for how many miles the car will travel in 8 hours.
d = rt
d = r * t
d = 60 * 8
d = 480

So the car will travel 480 miles in 8 hours

Another way to think about this is that you know the car traveled 240 miles in 4 hours and the question is wanting to know how far the car will travel in 8 hours, which would be double the 4 hours so 240 + 240 = 480

8 0
3 years ago
PLEASE HELP LOOK AT THE PICTURE
hammer [34]

Answer:

x = 10

Step-by-step explanation:

-8(-3 + x) = -56

Distribute the -8 into the (-3 + x).

24 - 8x = -56

Subtract 24 from both sides.

-8x = -80

Divide both sides by -8.

x = 10.

Proof:

-8(-3 + x) = -56

Substitute variable.

-8(-3 + 10) = -56

Add inside parenthesis.

-8(7) = -56

Multiply.

-56 = -56

4 0
2 years ago
Read 2 more answers
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