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Function Worksheets - Page 3

Function Worksheets
  • Page 3
 21.  
If f (x) = | x - 13|, then what is the value of f(14)f(11) ?
a.
- 1 24
b.
- 27 2
c.
27 2
d.
1 2


Solution:

f (x) = | x - 13 |

f (14) = | 14 - 13 | = 1
[Substitute x = 14 in f(x).]

f (11) = |11 - 13| = |- 2| = 2
[Substitute x = 11 in f(x).]

So, f(14)f(11) = 1 / 2


Correct answer : (4)
 22.  
If f (x) = 2x + 4x2 + 5x3, then find the value of f (2) + f (3) + f (4).
a.
629
b.
509
c.
- 155
d.
- 275


Solution:

f (x) = 2x + 4x2 + 5x3

f (2) = 2(2) + 4(2)2 + 5(2)3 = 60
[Substitute x = 2 in f (x).]

f (3) = 2(3) + 4(3)2 + 5(3)3 = 177
[Substitute x = 3 in f (x).]

f (4) = 2(4) + 4(4)2 + 5(4)3 = 392
[Substitute x = 4 in f (x).]

So, f (2) + f (3) + f (4) = 629


Correct answer : (1)
 23.  
If f(x) = 6x3, then f(x + h) - f(x)h =
a.
18x2 + 18xh + 6h2
b.
- 18x2 + 18xh - h2
c.
- 18x2 + 18xh - 6h2
d.
18x2 + 18xh + h2


Solution:

f(x) = 6x3

f( x + h) = 6(x + h)3
[Substitute (x + h) for x in f(x).]

So, f(x+h)-f(x)h = 6(x + h)3 -  6x3h

= 18x2 + 18xh + 6h2
[Simplify.]


Correct answer : (1)
 24.  
If f(x) is any real function, then which of the following is true?
a.
f(x + y) = f(x) + f(y)
b.
f(x - y) = f(x) - f(y)
c.
f 2(x) = (f (x))2
d.
None of the above


Solution:

The choices A, B and D are not true in the case of any function f(x) always, which can be checked out by taking any random function.

Since f 2(x) is defined as [ f(x)]2, the choice C is true.


Correct answer : (3)
 25.  
If f (x) = x + 5, g(x) = (x + 5)2 then evaluate (f + g)(3).
a.
14
b.
72
c.
64
d.
22


Solution:

f(x) = x + 5, g(x) = (x + 5)2

f(3) = 3 + 5 = 8
[Substitute x = 3 in f(x).]

g(3) = (3 + 5)2 = 64
[Substitute x = 3 in g(x).]

So, (f + g)(3) = f(3) + g(3) = 8 + 64 = 72
[Use (f + g)(a) = f(a) + g(a).]


Correct answer : (2)
 26.  
If f(x) = 9x, g(x) = 2x2 then find the value of (f - g)(- 3).
a.
21
b.
15
c.
- 21
d.
- 15


Solution:

f(x) = 9x and g(x) = 2x2

f(- 3) = 9- 3 = - 3
[Substitute x = - 3 in f(x).]

g(- 3) = 2(- 3)2 = 18
[Substitute x = - 3 in g(x).]

So, (f - g)(- 3) = f(- 3) - g(- 3) = - 3 - 18 = - 21
[Use (f - g)(a) = f(a) - g(a). ]


Correct answer : (3)
 27.  
If g(x) = x + 7 , h(x) = x - 7 then find the value of (hg)(8).
a.
15
b.
15
c.
8
d.
1


Solution:

g(x) = x + 7and h(x) = x - 7

g(8) = 8 + 7 = 15 = 15
[Substitute x = 8 in g(x).]

h(8) = 8 - 7 = 1 = 1
[Substitute x = 8 in h(x).]

So, (hg)(8) = h(8) g(8) = (1)(15) = 15
[Use (fg)(a) = f(a) × g(a).]


Correct answer : (1)
 28.  
If f(x) = x - 2x - 3 and g(x) = 2 + f(x) then find the value of fg(0).
a.
1 3
b.
1 4
c.
1 8
d.
2


Solution:

f(x) = x - 2x - 3 and g(x) = 2 + f(x)

f(0) = 0 - 20 - 3 = 2 / 3
[Substitute x = 0 in f(x).]

g(0) = 2 + f(0) = 2 + 2 / 3 = 8 / 3
[Substitute x = 0 in g(x).]

So, fg(0) = 2383 = 1 / 4
[Use fg(a) = f(a)g(a).]


Correct answer : (2)
 29.  
If f(x) = 6 - x, g(x) = (130 - x)3 and h(x) = (630 - x)4 then find the value of (fg +gh +hf)(5).
a.
31 5
b.
51 6
c.
-63 2
d.
41 4


Solution:

f (x) =6 - x, g(x) = (130 - x)3, h(x) = (630 - x) 4

f (5) = 6 - 5 = 1 = 1
[Substitute x = 5in f(x).]

g (5) = (130 - 5)  3 = 125  3 = 5
[Substitute x = 5 in g(x).]

h (5) = (630 - 5)  4= 625  4 = 5.
[Substitute x = 5 in h(x).]

So, (fg +gh +hf ) (5) = f(5)g(5) +g(5)h(5) + h(5)f(5)
[Use (fg +gh +hf ) (a) = f(a)g(a) +g(a)h(a) + h(a)f(a) .]

= ( 1 / 5) + (5 / 5) + (5 / 1) = 1 / 5 + 1 + 5 = 31 / 5


Correct answer : (1)
 30.  
If f (x) = x2 + 5x + 9 and g(x) = x2 + 7x + 9 then what is the value of fg(5)?
a.
59
b.
4071
c.
59 69
d.
25


Solution:

f(x) = x2 + 5x + 9 and g(x) = x2 + 7x + 9

f(5) = (5)2 + 5(5) + 9 = 59
[Substitute x = 5 in f(x).]

g(5) = (5)2 + 7(5) + 9 = 69
[Substitute x = 5 in g(x).]

So, fg(5) = f(5) × g(5) = (59)(69) = 4071
[Use fg(a) = f(a) × g(a).]


Correct answer : (2)

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