Question

a.)Consider the function f (x) = 3x/ x^2 +1

i) Evaluate f (x+1), and f (x)+1. Explain the difference. Do the same for f (2x) and 2f (x).

ii) Sketch y = f (x) on the interval [−2, 2].

iii) Solve the equations f (x) = 1.2 and f (x) = 2. In each case, if a solution does not exist, explain.

iv) What is the domain of f (x)?

b.)Let f (x) = √x −1 and g (x) = x 2 −3.

i) Find f ◦ g (x) and g ◦ f (x), and then compare their domains.

ii) Find a function h(x) such that h ◦ f (x) = x for all x in the domain of f (x)

c.) Let f (x) = x^2 + x +3. Find the difference quotient and simplify

Answer #1

Find the values of a function f(x) if
f(x) = 2x + 5, for
f(2), f(4),
f(k), and f(x2 +
2)
The difference quotient of a function is given by:
limh0f(x)
fx+h-f(x)h . Find the
difference quotient of, f(x) = 2x + 3 and f(x) = x2 +
2
a. Prove that h(x) and k(x) are inverses of each other when
h(x) =x+213 and k(x) = 3x + 21

Let the function f and g be defined as f(x) = x/ x − 1 and g(x)
= 2 /x +1 . Compute the sum (f + g)(x) and the quotient (f/g)(x) in
simplest form and describe their domains.
(f + g )(x) =
Domain of (f+g)(x):
(f/g)(x) =
Domain of (f/g)(x):

Let f(x) = 3x^2+x. Find the difference quotient.
f(x+h)-f(x) / h

1)If f(x)=2x-2 and g(x)=3x+9, find the following. a)
f(g(x))=? b) g(f(x))=? c) f(f(x))=?
2)Let f(x)=x^2 and g(x)=6x-16. Find the following: a)
f(3)+g(3)=? b) f(3)*g(3)=? c) f(g(3))=? d) g(f(3))=?
3) For g(x)=x^2+3x+4, find and simplify
g(3+h)-g(3)=?
Please break down in detail. Please and Thank
you

1. Let f(x)=−x^2+13x+4
a.Find the derivative f '(x)
b. Find f '(−3)
2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded
to 2 decimal places.
f '(3)=
3. Let f(x)=(x^3+4x+2)(160−5x) find f ′(x).
f '(x)=
4. Find the derivative of the function f(x)=√x−5/x^4
f '(x)=
5. Find the derivative of the function f(x)=2x−5/3x−3
f '(x)=
6. Find the derivative of the function
g(x)=(x^4−5x^2+5x+4)(x^3−4x^2−1). You do not have to simplify your
answer.
g '(x)=
7. Let f(x)=(−x^2+x+3)^5
a. Find the derivative....

Let f(x)= 3x^2-6x+1. Express this quadratic function in the
standard form . Find the vertex, the minimum or maximum value of
function , x-intercepts, y-intercept, domain and range. Show your
table of values, and sketch the graph.

5. Part I
If f(x) = 2x 2 - 3x + 1, find f(3) - f(2).
A. 0
B. 7
C. 17
Part II
If G( x ) = 5 x - 2, find G-1(x).
A. -5x + 2
B. (x + 2)/5
C. (x/5) + 2
Please help me solve this problem and if you can please also
show or explain how you got that answer. Thank you! :)

Consider the function f (x) = x/(2x+1)*2 .
(i) Find the domain of this function. (Start by figuring out any
forbidden values!)
(ii) Use (i) to write the equation of the vertical asymptote for
this function.
(iii) Find the limits as x goes to positive and negative
infinity,
(iv) Find the derivative of this function.
(v) Find the coordinates at point A(..,…), where the
x-coordinate is 1. Use exact fractions, never a decimal
estimate.
(vi) Find the equation of the...

1. Given f(x)=2x^3-3x^2+4x+2, find (f^(-1))'(14).
Differentiate and Simplify
2. f(x)=ln(3x) e^(-x^2 ) (Answer with positive exponents
Integrate and Simplify 3. ∫▒(6x^2-5x)/√x dx

(i) Given the function f(x) = x3 − 3x + 2
(a) What are the critical values of f?
(b) Find relative maximum/minimum values (if any). (c) Find
possible inflection points of f.
(d) On which intervals is f concave up or down?
(e) Sketch the graph of f.
(ii) Find a horizontal and a vertical asymptote of f(x) = 6x .
8x+3

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 23 minutes ago

asked 29 minutes ago

asked 30 minutes ago

asked 42 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago