1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
monitta
3 years ago
10

True or False?In Exercise,determine whether the statement is true or false given that f(x) = In x.if it is false,explain why or

given an example that shows it is false.
f(x - 2) = f(x) - f(2), x > 2
Mathematics
1 answer:
kompoz [17]3 years ago
6 0

Answer:

The given statement is false.

Step-by-step explanation:

We are given the following in the question:

f(x) = \text{In } x

The given statement is

f(x - 2) = f(x) - f(2), x > 2

Putting the values on the right side of the given statement

f(x-2)\\=\text{ln }(x-2) \neq \text{ln }x - \text{ln }2

Thus, the given statement is false.

This can be explained with the help of an example:

For x = 3

f(x-2) = f(3-2) = f(1)\\=\text{ln }1 = 0\\f(x)-f(2)\\=\text{ln }3-\text{ln }2 \\=0.4054

You might be interested in
Help me fast!!!!!!!I need to finish this by next period
klio [65]

Answer:

-2/3

Step-by-step explanation:

Rise over run!  The slope rises twice and goes over 3 times.  The slope is negative so put a negative sign behind it.

3 0
2 years ago
Read 2 more answers
A shop sells sweets where every 3 sweet wrappers can be exchanged for one more sweet. Kelvin has enough money to buy only 19 swe
drek231 [11]

Answer:

Kelvin can get 6 free sweets

6 0
1 year ago
Solve and i give brainliest
Temka [501]

Answer:

0.25

Step-by-step explanation:

-9/6 divided by 3/-2 = 0.25

i am sorry

4 0
2 years ago
Read 2 more answers
5. What is the equation of a line with a y-intercept at (0,6) and a slope of 3?
andreev551 [17]

Answer:

A

Step-by-step explanation:

You're correct. The Y intercept is the B. And 3 the slope.

8 0
3 years ago
Please I need help with differential equation. Thank you
Inga [223]

1. I suppose the ODE is supposed to be

\mathrm dt\dfrac{y+y^{1/2}}{1-t}=\mathrm dy(t+1)

Solving for \dfrac{\mathrm dy}{\mathrm dt} gives

\dfrac{\mathrm dy}{\mathrm dt}=\dfrac{y+y^{1/2}}{1-t^2}

which is undefined when t=\pm1. The interval of validity depends on what your initial value is. In this case, it's t=-\dfrac12, so the largest interval on which a solution can exist is -1\le t\le1.

2. Separating the variables gives

\dfrac{\mathrm dy}{y+y^{1/2}}=\dfrac{\mathrm dt}{1-t^2}

Integrate both sides. On the left, we have

\displaystyle\int\frac{\mathrm dy}{y^{1/2}(y^{1/2}+1)}=2\int\frac{\mathrm dz}{z+1}

where we substituted z=y^{1/2} - or z^2=y - and 2z\,\mathrm dz=\mathrm dy - or \mathrm dz=\dfrac{\mathrm dy}{2y^{1/2}}.

\displaystyle\int\frac{\mathrm dy}{y^{1/2}(y^{1/2}+1)}=2\ln|z+1|=2\ln(y^{1/2}+1)

On the right, we have

\dfrac1{1-t^2}=\dfrac12\left(\dfrac1{1-t}+\dfrac1{1+t}\right)

\displaystyle\int\frac{\mathrm dt}{1-t^2}=\dfrac12(\ln|1-t|+\ln|1+t|)+C=\ln(1-t^2)^{1/2}+C

So

2\ln(y^{1/2}+1)=\ln(1-t^2)^{1/2}+C

\ln(y^{1/2}+1)=\dfrac12\ln(1-t^2)^{1/2}+C

y^{1/2}+1=e^{\ln(1-t^2)^{1/4}+C}

y^{1/2}=C(1-t^2)^{1/4}-1

I'll leave the solution in this form for now to make solving for C easier. Given that y\left(-\dfrac12\right)=1, we get

1^{1/2}=C\left(1-\left(-\dfrac12\right)^2\right))^{1/4}-1

2=C\left(\dfrac54\right)^{1/4}

C=2\left(\dfrac45\right)^{1/4}

and so our solution is

\boxed{y(t)=\left(2\left(\dfrac45-\dfrac45t^2\right)^{1/4}-1\right)^2}

3 0
3 years ago
Other questions:
  • The graph illustrates a reflection of . What is the line of reflection?
    12·2 answers
  • (02.02 LC)<br> If g(x) = x2 – 4, find g(5)
    13·2 answers
  • You bought a large container of fruit punch. The label on the container says there are 128 fluid ounces of fruit punch in the co
    11·2 answers
  • How do I solve the problem 7(p + 3q) Please show how you go the answer.
    5·2 answers
  • Is the product of -5 +x and x+4 equal to the product of 5+x and x-4? Explain your answer.
    5·2 answers
  • Rhonda deposited $3000 in an account in the Merrick National Bank, earning 4.2% interest, compounded annually. She made no depos
    12·1 answer
  • The function f(x) = 2x 26 represents the distance a flock of birds travels in in miles. The function g(x) = x − 1 represents the
    8·1 answer
  • can anyone help me to get the answers please its important 5. An item marked at ₹ 340 is sold for ₹ 324. What is the discount? 6
    13·1 answer
  • Which reason best explains why m^10n^3 is NOT equal to (mn)^13?
    12·1 answer
  • If Q = {all perfect squares less than 30} and p={ all odd numbers from 1 to 10}
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!