Assignment# 1
Q1: If f(x) = π₯2- 4x+6 Find:
a) f(0)
b) f(3)
c) f(-2)
d) f(4)
Q2: If f(x) = π₯−1
π₯+1
Find:
a) f(0)
b) f(-1)
c) f(-4)
d) f(8)
Also show that f (1/x) = -f(x) and f (- 1/x) = - 1/ f(x)
Q3: Determine the domain of each of the following functions:
a) y = π₯2+ 4
b) y = √π₯2 + 4
c) y = √π₯2 − 4
π₯
d) y =
e) y =
π₯+3
2π₯
(π₯−2)(π₯+1)
1
f) y = √9−π₯2
π₯2− 1
g) y = π₯2+ 1
Q4: Draw the graph of the following functions for -5 ≤ x ≤ 5:
a) f(x) = −π₯2+ 1
b) f(x) = 5−π₯2
c) f(x) = - 4√π₯
d) f(x) = |x-3|
Q5: Calculate the Limit of the following function:
lim
π₯2 − 4π₯ + 4
2π₯→2 π₯ + π₯ − 6
You are required to solve Q5 using both the methods that were discussed in the class.
1) Factorize the denominator and cancel the function that is causing a Zero.
2) Calculate one-sided limits to find if the limit exists.
Q6: Whether the function is even, odd, or neither. Give reasons for your answer.
a) ππ(π₯) = π₯2 + 1
b) ππ(π₯) = π₯3 + π₯
c) ππ(π₯) = 1
π₯2−1
d) β(π‘) = 2π‘ + 1
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