MTH101 ASSIGNMENT 1 SOLUTION SPRING 2023
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SOLUTION:
QUESTION 1:
SOLUTION:1

The domain of
g(x) =  x^2.
In general, the domain of a polynomial function is all real numbers, so g(x) = x^2 is defined for all real values of x.
The domain of
f(x) = 3 / √x.
The denominator √x cannot be zero since division by zero is undefined
√x > 0
Squaring both sides, we get:
x > 0
So the domain of f(x) is all positive real numbers (x > 0).
The range of g(x) = x^2 is all non-negative real numbers (y ≥ 0) because squaring any real number yields a non-negative result.
Therefore, the domain of fog(x) is the set of all real numbers x such that x ≥ 0.
In interval notation, the domain of fog(x) is [0, +∞).

QUESTION 2:
SOLUTION 2:
A function is continuous if the following three conditions are satisfied:
•    The meaning is definite at that point.
•    The limit of the function exists as t approaches that point.
•    The worth of the meaning at that point is equivalent to the limit.
Note: In above conditions, the first condition must be fulfilled for further calculations.
The meaning is distinct at t = 2:
In the denominator (t - 2),
put t = 2,
 we get 0 in the denominator, which is undefined. Therefore, the function is not defined at t = 2.
Since the first condition is not satisfied (the function is not defined at t = 2), so the function f(t) = |t - 2| / (t - 2) is not continuous at t = 2.

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