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Score:
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Date:
EXERCISE 1.1 FUNCTIONS
A. For each of the following functions,
1. f(x) = 7x
2
+ 4x โ 1
a) f (-1/3) = 7(-1/3)
2
+ 4(-1/3) โ 1
f (-1/3) = 7/9- 4/3 โ 1 = 7/9 โ 12/9 -9/9 = -14/9
b) f (5) = 7(5)
2
+ 4(5) โ 1
f (5) = 175 + 20 โ 1 = 194
c) f(7x
2
) = 7(7x
2
)
2
+ 4(7x
2
) โ 1
f(7x
2
) = 7(49x
4
) + 28x
2
โ 1 = 343x
4
+ 28x
2
-1
d) f(x) + f(h) = 7(x)
2
+ 4(x) โ 1 + [7(h)
2
+ 4(h) โ 1]
f(x) + f(h) = 7x
2
+ 4x โ 1 + 7h
2
+ 4h - 1
f(x) + f(h) = 7x
2
+ 4x + 7h
2
+ 4h -2
f(x) + f(h) = 7h
2
+ 7x
2
+4h+4x -2
e) f(x
2
) +f(h
2
) = 7(x
2
)
2
+ 4(x
2
) โ 1 โ[7(h
2
)
2
+ 4(h
2
)-1]
f(x
2
) +f(h
2
) = 7x
4
+ 4x
2
โ 1 โ (7 h
4
+ 4h
2
โ 1)
f(x
2
) +f(h
2
) = 7x
4
+ 4x
2
โ 1 โ 7h
4
โ 4h
2
+1
f(x
2
) +f(h
2
) = 7x
4
+ 4x
2
โ 7h
4
- 4h
2
f(x
2
) +f(h
2
) = 7x
4
โ 7h
4
- 4h
2
+ 4x
2
2. f(x) = 7x
3
- 5
a) f (-1/3) = 7(-1/3)
3
-5
f (-1/3) = 7(-1/27) -5 = -142/27
b) f (5) = 7(5)
3
-5
f (5) = 7(125) -5 = 870
c) f(7x
2
) = 7(7x
2
)
3
-5
f(7x
2
) = 7(343x
6
) -5 = 2401 x
6
-5
d) f(x) + f(h) = 7(x)
3
-5 + [7(h)
3
-5]
f(x) + f(h) = 7x
3
- 5 + 7h
3
-5
f(x) + f(h) = 7x
3
-5 +7h
3
- 5
f(x) + f(h) = 7x
3
+ 7h
3
-10
f(x) + f(h) = 7(x
3
+ h
3
) -10
e) f(x
2
) - f(h
2
) = 7(x
2
)
3
โ 5 โ [7(h
2
)
3
-5]
f(x
2
) - f(h
2
) = 7x
6
โ 5 โ (7h
6
-5)
f(x
2
) - f(h
2
) = 7x
6
โ 5 โ 7h
6
+ 5
