Question

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 interval notation.)

Answer #1

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...

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...

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...

Consider the function on the interval (0, 2π). f(x) = sin(x)
cos(x) + 4. (A) Find the open interval(s) on which the function is
increasing or decreasing. (Enter your answers using interval
notation.) (B) Apply the First Derivative Test to identify all
relative extrema.

f(x)=1x−2 and g(x)=x−7x+3. For each function h given below, find
a formula for h(x) and the domain of h. Use interval notation for
entering the domains.
a) h(x)=(f∘g)(x). h(x) = Domain =
b) h(x)=(g∘f)(x). h(x) = Domain =
c) h(x)=(f∘f)(x). h(x) = Domain =
d) h(x)=(g∘g)(x). h(x) = Domain =

Find the derivatives of each of the following functions. DO NOT
simplify your answers.
(a) f(x) = 103x (3x5+ x − 1)4
(b) g(x) = ln(x3 + x) /
x2 − 4
(c) h(x) = tan-1(xex)
(d) k(x) = sin(x)cos(x)

Consider the function below. (If an answer does not exist, enter
DNE.)
f(x) = 1/2x^(4) − 4x^(2) + 3
(a)
Find the interval of increase. (Enter your answer using interval
notation.)
Find the interval of decrease. (Enter your answer using interval
notation.)
(b)
Find the local minimum value(s). (Enter your answers as a
comma-separated list.)
Find the local maximum value(s). (Enter your answers as a
comma-separated list.)
(c)
Find the inflection points.
(x, y) = (smaller x-value)
(x, y) =...

Find the derivative of the function using the definition of
derivative.
g(x) =
sqrt 9 −
x
g' (x) =
State the domain of the function. (using interval notation.)
State the domain of its derivative. (using interval notation.)

find the following for the function f(x)=3x^2+4x-4
a. f(0) b. f(3) c. f(-3) d. f(-x) e. -f(x) f. f(x+2) g. f(4x) h.
f(x+h)

f(x)=x2+9 and g(x)=x2-8, find the
following functions. a. (f * g) (x); b. (g * f)(x) c. (f *
g)(4);
d. (g * f)(4)

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