Compute the inner product ≤ p(x), q(x) >= p(xo)q(x0) + p(x₁)q(x₁) + p(x₂)q(x₂) where Xo = -1 p(x) = 1 + x² x₁ = 0 q(x) = 1x2x² x₂ = 1

Q: Rewrite c(x) = (x ^ 2 + 5x + 2)/(x - 3) in the form y = q(x) + (r(x))/(b(x)) has degree less than b.

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Q: Question1 Discuss the following terms with examples. invertible matrix, subspace, rank, column space

A: We are given some terms related to linear algebra: invertible matrix, subspace, rank, column space…

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: 4 find the difference quoitent of... f(x) = -√x-19

A: To find the difference quotient of the following function.fx=x-19

Q: Show that f(x) = (3x + 2)/(5x-1) is invertible. Determine the domain and range of f and f-1.

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Q: If f(x) = x* + 7, g(x) = x - 5, h(x) = Va, then fo g(x)= go f(x)= ho g(x)= %3D

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Q: What is the quotient when f(x) = 6x¹ − 2x³ + x² − 3x + 1 is divided by g(x) = x² + x -2 in Z₂[x]?

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Q: (ii) tank (In x) = x²-1 x² +1

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Q: f(g(h(x)))=

A: Givenf(x)=x4+5, g(x)=x-4 and h(x)=x

Q: given that f(x) =x-1, and g(x) =2x2 -1, determine (g (dot product) f)(x)     i put "(dot…

A: The given function is: f(x)=x-1           and             g(x)=2x2-1

Q: Find f(x) and g(x) such that h(x) = (f o g)(x). Let g(x) = 3x + 1. 1 h(x) = V3x + 1 f(x) =D

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Q: Let f(x)=√(x+1/x),g(x)=2/√(x-1) and h(x)=x^2+1 Describe the domains of f(x) and g(x) . Find…

A: We have to find domain

Q: Let g(x) = VT + 3.

A: Given,  g(x)=x2+3

Q: Let f(2) = x² +1 and g(z) = z² - 1 Then (fo f)(z) -X (fo g)(x) (go )(x) : x*4-x^2+1 x*4+x^2-1 Note:…

A: Consider the following functions: fx=x2+1gx=x2-1 ffx=x2+12+1=x4+2x2+1+1=x4+2x2+2…

Q: Find f(x) and g(c) such that h(x)=(f•g)(x) h(x)=(x^2+7)^5

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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: D ut he the plane 23 x=8 O Find arector in the plane X= 8 slone 3/5. Give avectar with unit per…

A: Use vector equation

Q: Let f(x)=2x+3 and g(x)=x+√x+2 Find f+g   (f*g)(x)

A: Given function is f(x)=2x+3 and g(x)=x+√x+2

Q: Find f (x). f(x) = 2 In (1 + 7x?) f(x) = %3D

A: f(x)=2ln(1+x2 ) Differentiating w.r.t x both sides, we have f'(x)=2ddx (ln(1+x2))…

Q: Find the zeros of the polynomials f (x)=x'-5x² – 2x + 24, If it is given that the product of its two…

A: *to find:- roots of the given equation.

Q: g(x)= f (x)-(f(x))" +(f (x))* for all xeR. Prove that f (x) and g(x) increase or decrease together.

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Q: Make the composition (f o g) (x) with the function f (x) = x ^ 2 + 2 -2 and g (x) = √x

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