7x + 4 3x - 4 Consider the functions f(x) = and g(x) = x+3 7-X (a) Find f(g(x)) (b) Find g(f(x)) (C) Determine whether the functions f and g are inverses of each other. ary (a) What is f(g(x))? f(g(x)) = (Simplify your answer.) Give any values of that need to be excluded from f(g(x)). Select the correct choice below and fill in any a ols > ОА. XF (Use a comma to separate answers as needed.) O B....
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...
Let f(x)=7x-8/3 and g(x)=3x+8/7. Find (f o g)(x) and (g o f)(x).
7x - 4 (1 point) Let f(x) = - 1. Find the open intervals on which f is concave up (down). Then determine the x-coordinates of all inflection x+4 points of f. 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection points occur at x = Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as...
I need these questions all solved please.
(11) Let f(x) x3 - 1 and g(x) = 25 sin 3r (a) What is the range of g(f(x))? Justify your answer (b) If h(r) f(g(x)) compute h'(x) (c) If t(x) ef(r) compute t'(x). (d) Obtain f'() from first principles 6 marks 6 marks 6 marks 6 marks 3. (e) Obtain the equation of the line tangent to the curve y [6 marks f(x) at (12) In this question, f(x)= r+2)2 2r (a)...
Let f(x) = 7x + 1 be the function such that f(x) = 6x2 + 2-1 n2". n=0 Q6.1 10 Points 1 Using the well-known geometric series r" = , |* |< 1, find the formula of Cand n=0 find the domain D of the function f. Please select file(s) Select file(s) Save Answer Q6.2 8 Points Using part Q6.1, find the value of the 102nd derivative of f(x) at x = 0; that is, find f(102)(0). Please select file(s)...
(x)). For each pair of functions f and g below, find f(g(x)) and g Then, determine whether f and g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) (a) f(x) = x + 4 (b) f(x) = - -, 0 3x x 5 ? g(x) = x - 4 f(g(x)) = 0 8(x)...
Please give a detailed answer and explanation.
Question 2 Let f(x) =x+x3 for x e [0, π] . what coefficients of the Trigonometric Fourier Series of f(x) are zero? Which ones are non-zeros? Why? Let g (x) = cos (r) + sin (x*). What coefficients of the Trigonometric Fourier Series of g(x) are zero? Which ones are non-zeros? Why? (a) (b)
For each pair of functions f and g below, find f(g(x)) and g(x)). Then, determine whether f and g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) (a) f(x) = -,x0 (b) f(x) = x + 4 $(x) = -,x+0 x 5 ? g(x) = -x + 4 $($(x)) = 0 (g(x)) =...
16. xyty Let f(x, y) = x3 + xy + y}, g(x, y) = x3 a. Show that there is a unique point P= (a,b) on 9(x,y) = 1 where fp = 1V9p for some scalar 1. b. Refer to Figure 13 to determine whether $ (P) is a local minimum or a local maximum of f subject to the constraint. c. Does Figure 13 suggest that f(P) is a global extremum subject to the constraint? 2 0 -3 -2...