Use the functions f and g in C[-1, 1] to find (f, 9), ||f||, ||9|l, and d(f, g) for the inner product (f, f(x) = 5x, g(x) = e¬* (a) (f, 9) (b) ||| (c) |l9|| (d) d(f, g)

Q: IT X) IS defined as foilows, ina (a) i( – 2), (D) (U), and (C) I(2). x? if x 0 (Simplify your…

A: Since the given function is a piecewise function therefore we need to take care of the branch of the…

Q: Differentiate: f(x) = e* +3* + In(4) A f)=e*+3in(3) +- f(x)= e+3 n(3) © fx)= e* +3* f(x) = e* +3* +=…

A: fx=ex+3x+ln4

Q: What are the x-intercept(s) of f(x) = x²7x+10 3(x-1)² a) There is no x-intercept. b) x = 1 (order 2)…

A:

Q: 3. Let d= = [( ) ( ) ( ) ( )], B = [1, 2, 2²), v = (¹). " (a) If f(x)=x²-3x+2, compute [ƒ(x)]ß. -1 2…

A: Our objective is given below:

Q: Show that f[x0, x1, x2] = f[x2, x1, xo].

A:

Q: 3. Find the largest domain (in R2) for the function In(3 + y) 1- x + y f (x, y) :

A: Let's find.

Q: 10) Calculate; Let f(x) = 3x + 1, g(x) = 4x-7 a) f(3) + g(4) b) f(x)-g(x) c) f(2)* g(-3)

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Q: Let f(x, y) /150- 4а2 — 2у? 4x? – 2y? Evaluate f(1, 3)

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Q: The zeros for Ax) = x-4x-9x + 36x are 1) (0,+3,4) 2) (0,3,4) 3) (0,±3,-4) 4) (0,3,-4)

A: Using method of synthetic division to find factors of f(x).

Q: The integral 2a12 + 5x° is equal to -dx 3 x5 + x3 +1 (a) -25 + C (2) +2² + 1)* (b) z10 +C (1 + کے +…

A:

Q: Find dy of 67 2. 2. my

A: The given equation is   yx=x2+2y2+1(ln y)x The product rule for derivatives is expressed as…

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: Use synthetic division to find 1"(-1) and f"(-1) where f(x)= 3x'-8x + 5x-2x' + 5x +13

A: To find the f'''-1 and f4-1 Given that the  fx=3x7-8x6+5x4-2x3+5x+13 f'x=21x6-48x5+20x3-6x2+5…

Q: If f is invertible and f(- 15) = 6, then %3D | f-(6) and (f( – 15))¯ -1 %3D

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Q: xux-yuy+y2u=y2x find the general solution

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Q: find f c^) : 2x+3 5X+4

A: Topic :- Functions

Q: 20) For the the function f(x) 5x-2, find f(4a+ 1) A) a-1 C) 9a-3 B) 20a - 1 E) 20a + 3 D) 9a – 1

A: Given that  f(x)=5x-2 Find f(4a+1)

Q: Find the domain off (g (x)) if f (x) = B D (-∞, 2) U (5, ∞] (2,27) U (27, co ) [2,27) U (27, ∞ ) [2,…

A:

Q: 10. Differentiate each function. a) y= -3x² + 4x- 5 b) f(x)=6x-1- 5x-2 ) flx)= 4\x d) y= (3x² –…

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Q: Suppose that I'm (f`∞x) = (x (24-1) and f(0) = 3-2i, f(1) = 6 -21, Find f(1+i)

A: Given that Imf'z=6x2y-1 To find: f(1+i).

Q: F(f)= 2 x-3 4x+1 a Find the dom F and dom F b-) Find ran F and ran F'

A:

Q: f(x) = -x² + ax + b, x < 2 (-ax + 7, x ≥ 2

A: Here we have to find the value of a and b such that,  f(x)=-x2+ax+b, x&lt;2-ax+7, x≥2 is continuous…

Q: find

A:

Q: 3. State the domain and range of f(x) = –- 2 D:(-x,0] А. D: В. D:[-2,0) C. D:[1,0) D. R:(-0,-1]…

A: To state the domain and range of,fx=-12-x-1

Q: D

A:

Q: The range of the function f(x, y) = 6 - 4 - x2 - y² is (-00, 6] o [4, 0) [4, 6] (-0,4] [6, 00)

A:

Q: 1. Let f(x) = 3x + 1, g(x) = 7 – 2x, and h(x) = x² – 4.x + 5. Find the following: a) (f + g)(2) b)…

A: 1. Given, f(x)=3x+1g(x)=7-2xh(x)=x2-4x+5

Q: What is the inverse of the function 2х + 1 f:R → R, f(x) ? 3.

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Q: 3x + 11y af If f(x, y) = then is : 3x – 11y dy - 66x (3x + 11y)² 66x (3x – 11y)² 66x (3x + 11y)2 66x…

A: Partial derivative

Q: Find all residues of the function z (2-2) not including the residue at infinity. "

A:

Q: Let f(x) = Vx and g(x) = x³ +1. Find 29 a) f(g(2)) b) g(f(4)) c) f(F(16)) d) g(g(0)) e) f(2+ h) f)…

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Q: Let f(x, y) = √175 – 3x² – 4y² Evaluate f(5,3)

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Q: 4 y-fx) 36) Use the graph of the quadratic function to write it as: f(x)-a(x -h)'+k 26 -4-2

A: The graph is downwards parabola whose equation is (y-k)=a(x-h)^2, where (h,k) is the vertex of…