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scZoUnD [109]
3 years ago
6

Which pair of functions have the same domain?

Mathematics
2 answers:
Alecsey [184]3 years ago
7 0

Answer:

It’s option three because both of their domains are all real numbers

Step-by-step explanation:

devlian [24]3 years ago
5 0

Answer:

i think its 3

Step-by-step explanation:

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I will mark you BRAINLIEST if you give correct step by step answer
vova2212 [387]

(i)

f(x) = x^2\\\\\frac{f(x +h) - f(x)}{h} = \frac{(x + h)^2 - x^2}{h} = \frac{x^2 + 2xh + h^2 - x^2}{h} = \frac{2xh + h^2}{h} = \frac{h(2x + h)}{h} = 2x + h

(ii)

f(x) = 3x + 5\\\\\frac{f(x + h) - f(x)}{h} = \frac{3(x + h) + 5 - (3x + 5)}{h} = \frac{3(x + h) + 5 - 3x - 5}{h} = \frac{3x + 3h + 5 - 3x - 5}{h} = \frac{3h}{h} = 3

(iii)

f(x) = x^2 + 3x + 6\\\\\frac{f(x + h) - f(x)}{h} = \frac{(x + h)^2 + 3(x +h) + 6 - (x^2 + 3x + 6)}{h} = \frac{x^2 + 2xh + h^2 + 3x + 3h + 6 - x^2 - 3x - 6}{h} = \frac{2xh + h^2 + 3h}{h} = \frac{h(3x + h + 3)}{h} = 2x +h + 3

(iv)

f(x) = x^3 + 1\\\\\frac{f(x + h) - f(x)}{h} = \frac{(x + h)^3 + 1 - (x^3 + 1)}{h} = \frac{(x + h)^3 + 1 - x^3 - 1}{h} = \frac{x^3 + 3x^2h + 3xh^2 + h^3 + 1 - x^3 - 1}{h} = \frac{3x^2h + 3xh^2 + h^3}{h} = \frac{h(3x^2 + 3xh + h^2)}{h} = 3x^2 + 3xh + h^2

8 0
3 years ago
Discontunuity of f(x) = x^2 plus 2x over x plus 2
Lina20 [59]

Answer:

When we have a function like:

f(x) = \frac{g(x)}{h(x)}

This function will have a discontinuity only if it diverges, and a divergence can happen when the denominator is equal to zero and the numerator is different than zero.

In this case, we have the equation:

f(x) = \frac{x^2 + 2*x}{x + 2}

Here the denominator is:

h(x) = x + 2

This is equal to zero when:

x + 2 = 0

x = -2

Now we need to see what happens with the numerator when x = -2

g(-2) = (-2)^2 + 2*(-2) = 0

Is equal to zero.

Then we need to see the limit when x -> -2, and use the L'Hopital theorem.

\lim_{x \to \ - 2} \frac{x^2 + 2*x}{x + 2}

Because we have zero over zero at that point, we need to look at the quotients of the derivatives of both numerator and denominator.

\lim_{x \to \ - 2} \frac{2*x+ 2}{ 2} = \frac{2*-2 + 2}{2} = -1

Then the function does not diverge, then the function has no discontinuity.

We also could look at the graph of f(x) to see it:

Our function is a linear function, and this is because the numerator is x times the denominator, then the function is:

f(x) = x.

8 0
3 years ago
A TV that normally cost $800 is on sale for 33% off. There is a 6% sales tax on the purchase. What is the final cost of the TV?​
UNO [17]

Answer:

$568.16

Step-by-step explanation:

3 0
3 years ago
Simplify 4!<br><br> A. 24<br> B. 10<br> C. 9<br> D. 4
professor190 [17]

Answer:

D

Step-by-step explanation:

5 0
3 years ago
Nancy thinks the answer to the question 1/4 divided by -2/3 is 3/8 is next correct explain why or why not be sure to use complet
stiks02 [169]

Answer:

  Her sign is in error. The answer is -3/8.

Step-by-step explanation:

Nancy's answer has the correct magnitude. It is obtained by multiplying 1/4 by -3/2. However, the sign of that product will be negative. Nancy has reported a positive answer, so <em>it is incorrect</em>.

6 0
3 years ago
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