Ask question

Ask question

All categories

3 years ago

15

2. Evaluate the function (3pts each) f(x) = 2x2 -*+5 a) f(-2) b) f(2x) c) f(x-1) 3. Find the domain of the function. (5 pts each

) 7X-5 a) f(x) = Vax- x²1 b) g(x) = x25x+6 Domain: Domain: 4. Calculate the difference quotient on the following function. You must show work for credit. (5pts) f(x) = 3x2 - 5

1 answer:

Fofino [41]3 years ago

4 0

Answer:

2a : f(-2) = 15

2b : f(2x) = 8x² - 2x + 5

2c : f(x-1) = 2x² - 5x + 8

3a : x > 1/3

3b : x <> {2,3}

4 : 6x

Step-by-step explanation:

2a.

2×(-2)² - (-2) + 5 = 2×4 + 2 + 5 = 15

2b.

2×(2x)² - 2x + 5 = 2×4x² - 2x + 5 = 8x² - 2x + 5

2c.

2×(x-1)² - (x-1) + 5 = 2×(x² - 2x + 1) - x + 1 + 5 =

= 2x² - 4x + 2 - x + 1 + 5 = 2x² - 5x + 8

3a.

the square root is not defined for negative values, which would happen for any x < 1/3. and for x=1/3 the expression would be a division by 0, which is also undefined.

so, all that is left is x>1/3.

3b.

we must avoid a division by 0. everything else is well defined.

so, when is that expression x² - 5x + 6 = 0 ?

solution for a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/2a

a = 1

b = -5

c = 6

x = (5 ± sqrt(25 - 24))/2 = (5 ± sqrt(1))/2 = (5 ± 1)/2

x1 = (5+1)/2 = 6/2 = 3

x2 = (5-1)/2 = 4/2 = 2

so, these values must be avoided for x. everything else is valid.

4.

(f(x+h) - f(x))/h

for h going to 0.

f(x) = 3x² - 5

f(x+h) = 3×(x+h)² - 5

f(x+h) - f(x) = 3×(x² + 2hx + h²) -5 - 3x² + 5 =

= 3x² + 6hx + 3h² - 3x² = 6hx + 3h²

=>

(f(x+h) - f(x))/h = (6hx + 3h²)/h = 6x + 3h = for h 0 = 6x

You might be interested in

The cost of purchasing a bag of rice is partly constant and partly varies inversely as the square root of the number of people d

algol [13]

Answer:

(a) 160 Naira

(b) Undefined

Step-by-step explanation:

Given

Let:

$y \to$ cost of bag of rice

$x \to$ people demanding the bag

So, we have:

$y\ = \frac{k}{\sqrt x} + c$ ---- The variation

$y = 100; x = 36$

$y = 150; x = 144$

We have:

$y\ = \frac{k}{\sqrt x} + c$

When: $y = 100; x = 36$

$100 = \frac{k}{\sqrt {36}} + c$

$100 = \frac{k}{6} + c$ -- (1)

When: $y = 150; x = 144$

$150 = \frac{k}{\sqrt {144}} + c$

$150 = \frac{k}{12} + c$ --- (2)

Subtract (1) from (2)

$150 - 100 = \frac{k}{12} - \frac{k}{6} + c - c$

$50 = \frac{k}{12} - \frac{k}{6}$

Multiply through by 12

$600 = k - 2k$

$600 = -k$

$k = -600$

To solve for x, we have:

$100 = \frac{k}{6} + c$ -- (1)

This gives:

$100 = \frac{-600}{6} + c$

$100 = -100 + c$

$c = 100 + 100$

$c = 200$

So, the equation is:

$y\ = \frac{k}{\sqrt x} + c$

$y = -\frac{600}{\sqrt x} + 200$

Solving (1): y; when x = 225

We have:

$y = -\frac{600}{\sqrt x} + 200$

$y = -\frac{600}{\sqrt {225}} + 200$

$y = -\frac{600}{15} + 200$

$y = -40 + 200$

$y = 160$

Solving (2): x; when x = 200

We have:

$y = -\frac{600}{\sqrt x} + 200$

$200 = -\frac{600}{\sqrt x} + 200$

Collect like terms

$\frac{600}{\sqrt x} = 200 - 200$

$\frac{600}{\sqrt x} =0$

Cross multiply

$600 =0 * \sqrt x$

$600 =0$

<em>x is undefined</em>

7 0

3 years ago

in a continuous data the median class is 40-50. If the cumulative frequencies of the premedian class is one half of the sum of t

Ede4ka [16]

To find the median, add up the frequency column to find how many trains there were in total. There were 44 trains in total in this grouped frequency table, so work out 44 + 1 2 = 45 2 = 22.5. The median is therefore between the 22nd and 23rd values.

3 0

3 years ago

Water is being pumped into a reservoir tank. The total amount of water (w) after an amount of time (t) is given by the equation

pychu [463]

Answer:

it will take 8 minutes

Step-by-step explanation:

Here, we want to

calculate the amount of time taken to fill the tank given the total amount of water in the tank.

Mathematically, the formula go

use is ;

w= 100 + 55t

540 = 100 + 55t

55t = 540-100

55t = 440

t = 440/55

t = 8

7 0

3 years ago

Evaluate the summation of negative 5 n minus 1, from n equals 3 to 12..

USPshnik [31]

The correct answer for the question that is being presented above is this one: "B. -385." Evaluate the summation of negative 5 n minus 1, from n equals 3 to 12 equals B. -385

-5n - 1 where n = 3 to 12.
n = 3 = -16
n = 4 = -21
n = 5 = -26
n = 6 = -31
n = 7 = -36
n = 8 = -41
n = 9 = -46
n = 10 = -51
n =11 = -56
n = 12 = -61

Total = B. -385

6 0

4 years ago

Read 2 more answers

Please help, I will give brainliest, I am struggling badly.

eimsori [14]

Answer:

y= -3/5 x

Step-by-step explanation:

I hope this helps!!!

7 0

3 years ago