Desklib Study Material Solutions

1 Question 1.
Apply complex arithmetic rule : (a + bi) (c + di) = (ac − bd) + (ad + bc) i
(8 − 9i)(2 − 4i) + (5 − 6i) = (8 · 2 − (−9) · (−4)) + (8 · (−4) + (−9) · 2)i + 5 − 6i
= (16 − 36) + (−50)i + 5 − 6i
= −15 − 56i
2 Question 2.
Apply complex arithmetic rule : a+bi
c+di = (c−di)(a+bi)
(c−di)(c+di) = (ac+bd)+(bc−ad)i
c2 +d2
3 − √5i
2 + √3i =
(3 · 2 + (−√5) √3) + (−√5 · 2 − 3√3) i
22 + (√3)2
= 6 − √15
7 + −2√5 − 3√3
7 i
3 Question 3.
For a maximum or a minimum f’(x)=0.
d
dx (−2x2 + 4x + 7) = 0
−4x + 4 = 0
x = 1
At this value of x=1, d2
dx2 f (x) = −4 < 0 and hence this gives a maximum
value of f(1)=−2(1)2 + 4(1) + 7 or f(1)=9.
4 Question 4.
(5x5y−4)2 =
( 5x5
y4
)2
Apply exponent rule:
( a
b
)c
= ac
bc we get :
(5x5y−4)2 =
(5x5)2
(y4)2
= 25x10
y8
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5 Question 5.
According to the graph the domain of the function is [-3,3) ∪[4, ∞) and the
range is [−9, ∞).
6 Question 6.
Subtracting elements in matching positions :

4 7 4
9 9 6
6 9 7

 −


−9 5 7
3 2 4
9 −1 4

 =


4 − (−9) 7 − 5 4 − 7
9 − 3 9 − 2 6 − 4
6 − 9 9 − (−1) 7 − 4




4 7 4
9 9 6
6 9 7

 −


−9 5 7
3 2 4
9 −1 4

 =


13 2 −3
6 7 2
−3 10 3


7 Question 7.
There is no question of continuity at x=3 since the function is not defined at
x=3.
8 Question 8.
By average rate of change we calculate ∆f (x)
∆x , where ∆x = (14 − 5) = 9, and
∆f (x) = f (14) − f (5) = −702 hence average rate of change is −702
9 or -78.
9 Question 9.
For the function f ◦ g(x), we need √x − 6 6 = 0 also for square root we need
x − 6 ≥ 0. Hence we need x − 6 > 0 or x > 6. Hence our Domain is (6, ∞).
And our function f ◦ g(x) = −3√x−6 , x > 6.
10 Question 10.
The critical points i.e the points where the derivatives are zero are x=0,1,2.5
The point x=0 is a local maxima, x=1 is an inflection point and x=2.5 is a
local minima.
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