Finding the domain of a composite function involving radicals
Find the domain of
Because we cannot take the square root of a negative number, the domain of
is
Now we check the domain of the composite function
The domain of this function is
To find the domain of
we ask ourselves if there are any further restrictions offered by the domain of the composite function. The answer is no, since
is a proper subset of the domain of
This means the domain of
is the same as the domain of
namely,
Decomposing a composite function into its component functions
In some cases, it is necessary to decompose a complicated function. In other words, we can write it as a composition of two simpler functions. There may be more than one way to
decompose a composite function , so we may choose the decomposition that appears to be most expedient.
Decomposing a function
Write
as the composition of two functions.
We are looking for two functions,
and
so
To do this, we look for a function inside a function in the formula for
As one possibility, we might notice that the expression
is the inside of the square root. We could then decompose the function as
We can check our answer by recomposing the functions.
We can perform algebraic operations on functions. See
[link] .
When functions are combined, the output of the first (inner) function becomes the input of the second (outer) function.
The function produced by combining two functions is a composite function. See
[link] and
[link] .
The order of function composition must be considered when interpreting the meaning of composite functions. See
[link] .
A composite function can be evaluated by evaluating the inner function using the given input value and then evaluating the outer function taking as its input the output of the inner function.
A composite function can be evaluated from a table. See
[link] .
A composite function can be evaluated from a graph. See
[link] .
A composite function can be evaluated from a formula. See
[link] .
The domain of a composite function consists of those inputs in the domain of the inner function that correspond to outputs of the inner function that are in the domain of the outer function. See
[link] and
[link] .
Just as functions can be combined to form a composite function, composite functions can be decomposed into simpler functions.
Functions can often be decomposed in more than one way. See
[link] .
Section exercises
Verbal
How does one find the domain of the quotient of two functions,
Find the numbers that make the function in the denominator
equal to zero, and check for any other domain restrictions on
and
such as an even-indexed root or zeros in the denominator.
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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