Course: Pre-Calculus (4431)Assignment 1 solved, Sem:Spring, 2024

Course: Pre-Calculus (4431)                                     Semester: Spring, 2024

ASSIGNMENT No. 1

(Units: 1–4)

Q. 1   (a)     For each of the following statements, either prove it is true or give counter example to show it is false;                                                                                                           

1. The product of two rational numbers is always rational
2. The product of two rational numbers is always irrational.
3. The product of a non-zero rational and an irrational is always irrational.
4. The product of two irrational numbers is always rational

            (b)        Prove that if n is any positive integer, then + is irrational.

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Q. 2   (a)     Determine whether the following functions are even or odd:                   

                            

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         (b)     Given that f (x) = 2x + 1 and h(x) = 2x² + 4x + 1 find a function g such that, f(g(x)) = h(x)   

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Q. 3   (a)     Find all values of a such that      

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      (b)        Approximate the value for the following limit. Confirm your approximation using graphical evidence.

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