Question

Find the domain of the following function. Explain your reasoning and express your answer in interval notation.

f(x)= ln (x)/ (e^2x) -3

Answer #1

1a.
Find the domain and range of the function. (Enter your answer
using interval notation.)
f(x) = −|x + 8|
domain=
range=
1b.
Consider the following function. Find the composite
functions
f ∘ g
and
g ∘ f.
Find the domain of each composite function. (Enter your domains
using interval notation.)
f(x) =
x − 3
g(x) = x2
(f ∘ g)(x)=
domain =
(g ∘ f)(x) =
domain
are the two functions equal?
y
n
1c.
Convert the radian...

Find the domain for
Write your answer in interval notation.
Answer: _____________________________
Find the intervals of Increase for
Write your answer in interval notation. (Remember it will not
increase or decrease on an interval which is not in its
domain.)
Answer: _____________________________
Find the intervals of concave up for
y=x3−6x2−15x+4
Answer: ____________________________
Find the y-intercept
for y=x3−6x2−15x+4
Answer: ______________________________

Using interval notation, determine the largest domain over which
the given function is one‑to‑one. Then, provide the equation for
the inverse of the function that is restricted to that domain.
If two equally large domains exist over which the given function
is one‑to‑one, you may use either domain. However, be certain that
the equation for the inverse function you submit is appropriate for
the particular domain you choose.
f(x)=10−x
(Give your answer as an interval in the form (∗,∗).
Use...

4. Find the inverse function of f. State the domain and range
(in interval notation) of the
inverse function f exponent of −1 (x).
f(x) = 4 + 5x all over 3x − 6

Find the inverse function of f(x)= 1+2cos(x) and then find the
domain and the range of the function of both f and f^-1??
Find the inverse function of f(x)=sqrt(3-e^2x) and then find the
domain and the range of the function of both f and f^-1??

Write a Maclaurin series for the following function; put the
answer in sigma notation, and find the interval of convergence:
f(x) = 4x * ln(2+x)

Find each of the following functions. f(x) = 4 − 4x, g(x) =
cos(x)
(a) f ∘ g and State the domain of the function. (Enter your
answer using interval notation.)
(b) g ∘ f and State the domain of the function. (Enter your
answer using interval notation.)
(c) f ∘ f and State the domain of the function. (Enter your
answer using interval notation.)
(d) g ∘ g and State the domain of the function. (Enter your
answer using...

a) Find the domain and range of the following function:
f(x,y)=sin(ln(x+y))
b) sketch the domain.
c) on seperate graph, sketch three level curves

Consider the following function. (If an answer does not exist,
enter DNE.)
f(x) = 1 +
5
x
−
3
x2
(c) Find the local maximum and minimum values.
(d) Find the interval where the function is concave up. (Enter your
answer using interval notation.)
(e) Find the interval where the function is concave down. (Enter
your answer using interval notation.)
(f) Find the inflection point.
(x, y) =

1- If
?(?)=3?5?+29?5?+1
find the inverse function.
2- State the domain of the function ?(?)=8?−94?
3- State the domain of the function ?(?)=5?−83?+5 in interval
notation
4- State the domain of the function ?(?)=7?−8?−3
in interval notation.
5- State the domain of the function ?(?)=9?+1?2−3?−40
in interval notation
6- State the domain of the function ?(?)=8?+13?2−11?+8
in interval notation.
7- State the domain of the function ?(?)=8?−39?2+12?+13
in interval notation.

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