Let f(x) = 3x2and g(x) = 3-x
Evaluate
a. (fg)(5)
b. (flg)(5)
c. (f circle cymbol g) (5)
- see attatched picture
,
Given f(x)=3x^2,g(x)=3-x
(a) (fg)(x)=f(x)g(x)
=(3x^2)(3-x)
=9x^2-3x^3
Hence, (fg)(5)=9x(5^2)-3x(5^3)
= 9x25-3x125 = -150 ....(1)
(b) (f/g)(x)=f(x)/g(x)
=(3x^2)/(3-x)
Hence,(f/g)(5)=(3x5^2)/(3-5)
= -75/2.......(2)
(c) (fog)(x)=f{g(x)}
=f(3-x)
=3 x (3-x)^2
(fog)(5)= 3x(3-5)^2
= 3x4 = 12......(3)
( Please like if solution is helpful)
Let f(x) = 3x2and g(x) = 3-x Evaluate a. (fg)(5) b. (flg)(5) c. (f circle cymbol...
c. Evaluate ,f(z) dz with า the circle of radius 1 centered at the origin and traveled once counterclockwise ˊ们: (1-2 For real twith-1 < t < 1 and +12)-1 Explain why f(:)) has an expansion of the form in C , let f(z) be defined by fG)- a. b. Compute Uo(t), Ui(t), and Uz(t) in terms of t. c. Recalling that t is a real number smaller than 1 in absolute value, find the radius of convergence of this...
Let f(x) = 7x+2 and g(x) = 4x - 5. Find (f+g)(x). (f-9)(x), (fg)(x), and (x). Give the domain of each. (f+9)(x) = (Simplify your answer.) (f-9)(x) = (Simplify your answer.) (fg)(x) = (Simplify your answer.) (9) - [] (simplify your answer) The domain off+g is (Type your answer in interval notation.) The domain off-gis (Type your answer in interval notation.) The domain of fg is (Type your answer in interval notation) The domain of (Type your answer in interval...
15. Let g(x)= Vx + 3 and f(x)= 5cos( x ). Evaluate (fog")(5) . A. 5 B. -5 C. O D. 5/2 E. -5/2 F. None of the above
3. Let f, g : a, b] → R be functions such that f is integrable, g is continuous. and g(x) 〉 0 for all x є a,b]. Since both f, g are bounded, let K 〉 0 be such that |f(x) K and g(x) < K for all x E [a,b (a) Let n > 0 be given. Prove that there is a partition P of [a, b such that for all i 2. (b) Let P be a...
18 Let g(t) be defined by the following table: a. Evaluate g(5) b. Evaluate g(0). c. Is g(3) defined? Explain. 44. Let h(t) be defined by the following table: t hin a. Evaluate h(-2). b. Evaluate h(4). c. Is h(5) defined? 4.5 Explain "mo Paying Attention to InstructionsExercises 45 and 46 are intended to give you practice reading and paying attention to the instructions that accompany the problems you are working (45) a. Solve for x 2x + 3 =...
let f(x)=x^2 -3 and g(x)=2x+3 Evaluate. f(-2) Let f(x)=
Use for #4, 5. Let f(x) = 3* and g(x)= (1/2)". Find each function value. Circle the correct choice. 4. Find f(-2) a. 9 b. -9 c. = ICE d. - 5. Find g(-3) a. - b. 8 d. d. - 8 ( EX
3. Let f, g : a, bl → R be functions such that f is integrable, g is continuous. and g(x) >0 for al x E [a, b]. Since both f,g are bounded, let K> 0 be such that f(x)| 〈 K and g(x)-K for all x E la,b] (a) Let η 〉 0 be given. Prove that there is a partition P of a,b] such that for all i (b) Let P be a partition as in (a). Prove...
11. LetF(x, y) - (2xe), x + x-e)) and let C be the quarter-circle path from A to B in Figure 18. Evaluate 1-φ F . dr as follows: (a) Find a function f (x, y) such that F- G + V f, where G (0, x). (b) Show that the line integrals of G along the segments OA and OB are zero. (c) Evaluate I. Hint: Use Green's Theorem to show that B (0,4) A (4, 0) FIGURE 18
Find f+g, f-g, fg, and f/g and their domains. f(x) = 4 – x, g(x) = x2 – 3x Find (f + g)(x). Find the domain of (f + g)(x). (Enter your answer using interval notation.) Find (f - g)(x). Find the domain of (f - g)(x). (Enter your answer using interval notation.) Find (fg)(x). Find the domain of (fg)(x). (Enter your answer using interval notation.) Find (6)«). Find the domain of (x). (Enter your answer using interval notation.) Consider...