Functional Analysis Answers

value of 2-3*5+9 is

Calculate Time Complexity of following

(i)

F𝑜𝑟 (𝑖 = 1;𝑖 ≤ 𝑛; 𝑖 ∗ = 2)

{ 

𝑥 = 𝑥 + 1 

}

(ii)

𝑓𝑜𝑟 (𝑖 = 1;𝑖 ≤ 𝑛; 𝑖 + +)

𝑓𝑜𝑟 (𝑗 = 1;𝑗 ≤ 𝑛;𝑗 = 𝑗 ∗ 2)

{ 

… . 

… . 

}

What is the domain of the rational function f(x) = 2x²-7/ 3x + 5?

A. the set of all positive real numbers

B. the set of all real numbers except x= - 5/3

C. the set of all real numbers

D. the set of all real numbers except x= 5/3

Which of the following rational functions does not have a vertical asymptote?

A. g(x) = 2x+7/x+5

B. h(x) = 2x²+7/3x²-5

C. k(x) = 2x² - 7/3x-5

D. f(x) = 2/ x²+5

let H be finite separable hilbert space. show that H is unitarily isomorphic to cʳ for some r ∊ N.

If there are 20 items on his list on the 26thof March, and the number of items grows by

25% per day, how many items will he have on his list on April 9th?

Find all metrics on a set X consisting of two points. Consisting of one point only.

Let the functional f on R² be defined by f(x)= 4x-3y.Regard R² as a subspace of R³ given by z=0 determine all linear extension of f(x) from R² to R³

• Prove that C.V100√n-1

Let V be a Banach space and let M ⊆ V be a proper subspace of V (i.e. M not equal to V ). Prove that if v ∈ V and v /∈ M then there is a φ ∈ V* such that φ(v) = 1 and φ(w) = 0 for every w ∈ M.