Question

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

Answer #1

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....

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

. Let f(x) = 3x^5/5 −2x^4+1. Find the following:
(a) Interval of increasing:
(b) Interval of decreasing:
(c) Local maximum(s) at x =
d) Local minimum(s) at x =
(e) Interval of concave up:
(f) Interval of concave down:
(g) Inflection point(s) at x =

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! :)

1.
Calculate the following derivatives
(a) f′(x) where f(x) = e^2x sin(3x)
(b) g′(3π/4) where g(x) = sec(x) (simplify)

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) =...

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)

Given that f(x)=x^2-9 and g(x)=3x+16, find (g-f)(9), if it
exists.

Find (f −1 (a))' :
(a) f(x) = 2x 3 + 3x 2 + 7x + 4, a = 4
(b) f(x) = 2x + cos(x), a = 1

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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