MTH100 Incharge Dr Asif Ali by Ali Khan

Q02. Determine whether the function f(x) = 2/x is even or odd. Also, find its domain and range.

To determine whether the function f(x) = 𝑥 is even or odd, we can use the definitions:

Step 1: Check if the function is even or odd

1. Calculate f(−𝑥)

f(−𝑥)= −𝑥 = − 𝑥

2. -f(x) = - ( 𝑥) = - 𝑥

Step 2: Determine the domain

The function f(𝑥) = 𝑥 is defined for all real numbers except where the denominator is zero. Thus, the domain is:

Domain: (-∞, 0) U (0, ∞)

Step 3: Determine the range

The function f(x) = 2/x can take on all real values except for zero. As x approaches 0 from the left, F(x) approaches ∞, and as x approaches 0 from the right, f(x) approaches +∞ Therefore, the range is: Range : : (-∞, 0) U (0, ∞)

Summary

The function f(x) = 2/x is odd.

Domain: (-∞, 0) U (0, ∞)

Range: (-∞, 0) U (0, ∞)

Q03. Let f(x) = 5x + 3 and g(x) = 3x - 5 be the two functions then find the composite Functions (f o g) (x) and (g o f) (x).

Answer: First = (f o g) (x) F (g(x)) = f (3x-5) F (3x-5) = 5(3x-5) +3 = 15x -25 +3 = 15x – 22 Now: (g o f) (x) g (f(x)) = g ( 5x+ 3) = (3 (5x+ 3) -5) = 15x + 9 -15 = 15x+4

Q04. Solve the following system of equations by applying row operation. 3x, + 3x2 = 15

15x1 + 16x2 = 23

To solve the system of equations using row operations, let’s first write down the system in matrix form:

The system is:

3x1+ 3x2 = 15 15x1+ 16x2 = 23 In matrix form, this is: [ 3 16] [𝑥1 𝑥2] = [15 23]

Now, we’ll apply row operations to solve for X1 and X2