Question

Find the derivative of the function using the definition of derivative.

* g*(

sqrt 9 −
x |

* g'* (

State the domain of the function. (using interval notation.)

State the domain of its derivative. (using interval notation.)

Answer #1

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...

use
the definition of derivative to find the derivative of
f(x)= 2*sqrt(x-7)
show work please.

a) find the derivative of xcos(x^2) using
any method.
b) find the derivative of f(x) = sqrt(3-x) using only the
definition.

1. Consider the function.
f(x) = 6x − 9
(a) Find the inverse function of f.
(b) Graph f and f −1 on the same
set of coordinate axes.
(c) Describe the relationship between the graphs. The graphs of
f and f −1 are reflections of each
other across the line y =
(d) State the domain and range of f and f
−1. (Enter your answers using interval notation.)
2.
Consider the function.
f(x) = x+3/x
(a) Find the...

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...

State (precisely) the limit definition for the derivative of an
arbitrary function f(x) at the point
x0. Use the limit definition
to compute the derivative of the following
function: f(x) = 1/x^2

Using the derivative definition, point the derivative value for
the given function f(z)=3/z^2 Find in Z0=1+i and write x+iy
algebraically.

Q 1) Consider the following functions.
f(x) = 2/x, g(x) = 3x + 12
Find (f ∘ g)(x).
Find the domain of (f ∘ g)(x). (Enter your answer using interval
notation.)
Find (g ∘ f)(x).
Find the domain of (g ∘ f)(x). (Enter your answer using
interval notation.)
Find (f ∘ f)(x).
Find the domain of (f ∘ f)(x). (Enter your answer using
interval notation.)
Find (g ∘ g)(x).
Find the domain of (g ∘ g)(x). (Enter your answer using interval
notation.)
Q...

Use the formal definition of the derivative to find the
derivative of given function, ?(?) = 1 √1−? .

Suppose the function g(x) has a domain of all real
numbers except x = −8. The second derivative of
g(x) is shown below.
g ''(x) =
(x−1)(x + 5)
(x +
8)7
(a) Give the intervals where g(x) is concave up. (Enter your
answer using interval notation. If an answer does not exist, enter
DNE.)
(b) Give the intervals where g(x) is concave down. (Enter your
answer using interval notation. If an answer does not exist, enter
DNE.)
(c) Find...

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