Question

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) = x^{2}

(f ∘ g)(x)=

domain =

(g ∘ f)(x) =

domain

are the two functions equal?

y

n

1c.

Convert the radian measure to degree measure.

π |

3 |

1d.

Evaluate the sine, cosine, and tangent of the angle.

7π |

3 |

sin (7pie/3)

cos(7pie/3)

tan(7pie/3)

1e.

Solve the equation for θ, where

0 ≤ θ ≤ 2π.

(Enter your answers as a comma-separated list.)

4 cos^{2}(θ) = 3

θ =

Answer #1

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

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...

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...

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...

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??

The domain of the function g(x) is -1<x<6 and
the range is -5<y<10.
Find the domain and range of the following given functions.
a). the domain of y=g(x-4) is?
b.) the range of y=g(x)+2 is?

Find the domain of the following function. Explain your
reasoning and express your answer in interval notation.
f(x)= ln (x)/ (e^2x) -3

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...

Express the function f(t) = t, defined ONLY in the domain
0<t<3, as i) a half-range sine series and ii) a half-range
cosine series. In each case, confirm the value of f(t) at t=2.

Let f(x)=5−log(x+1), g(x)=x2−2x−4 and k(x)=5/(x−4).
(a) Find (fog)(x)(fog)(x) and its domain using the interval
notation.
(b) Find the inverse of the function ff.
(c) Find the function g/kg/k and its domain using the interval
notation.
(d) Simplify the expression
[k(x+h)−k(x)]/h[k(x+h)−k(x)]/h.

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