Answer:
Like terms, functions may be combined by addition, subtraction, multiplication or division.
Example 1. Given f ( x ) = 2x + 1 and g ( x ) = x2
+ 2x – 1 find ( f + g ) ( x ) and
( f + g ) ( 2 )
Solution
Step 1. Find ( f + g ) ( x )
Since ( f + g ) ( x ) = f ( x ) + g ( x ) then;
( f + g ) ( x ) = ( 2x + 1 ) + (x2
+ 2x – 1 )
= 2x + 1 + x2
+ 2x – 1
= x
2
+ 4x
Step 2. Find ( f + g ) ( 2 )
To find the solution for ( f + g ) ( 2 ), evaluate the solution above for 2.
Since ( f + g ) ( x ) = x2
+ 4x then;
( f + g ) ( 2 ) = 22
+ 4(2)
= 4 + 8
= 12
Example 2. Given f ( x ) = 2x – 5 and g ( x ) = 1 – x find ( f – g ) ( x ) and ( f – g ) ( 2 ).
Solution
Step 1. Find ( f – g ) ( x ).
( f – g ) ( x ) = f ( x ) – g ( x )
= ( 2x – 5 ) – ( 1 – x )
= 2x – 5 – 1 + x
= 3x – 6
Step 2. Find ( f – g ) ( 2 ).
( f – g ) ( x ) = 3x – 6
( f – g ) ( 2 ) = 3 (2) – 6
= 6 – 6
= 0
Example 3. Given f ( x ) = x2
+ 1 and g ( x ) = x – 4 , find ( f g ) ( x ) and ( f g ) ( 3 ).
Solution
Step 1. Solve for ( f g ) ( x ).
Since ( f g ) ( x ) = f ( x ) * g ( x ) , then
= (x2
+ 1 ) ( x – 4 )
= x
3
– 4 x2
+ x – 4 .
Step 2. Find ( f g ) ( 3 ).
Since ( f g ) ( x ) = x3
– 4 x2
+ x – 4, then
( f g ) ( 3 ) = (3)3
– 4 (3)2
+ (3) – 4
= 27 – 36 + 3 – 4
= -10
Example 4. Given f ( x ) = x + 1 and g ( x ) = x – 1 , find ( x ) and ( 3 ). f
g
⎛ ⎞ ⎜
⎝ ⎠
f
g
⎛ ⎞ ⎜
⎝ ⎠ ⎟ ⎟
Solution
Step 1. Solve for ( x ). f
g
⎛
⎜
⎝ ⎠
⎞
⎟
Since ( x ) = , then ( )
( )
f x
g x
f
g
⎛
⎜
⎝ ⎠
⎞
⎟
= ; x ≠ 1 1
1
x
x
+
−
Step 2 Find . ( ) 3 f
g
⎛ ⎞ ⎜ ⎟ ⎝ ⎠
Since = , then 1
1
x
x
+
− ( ) f x
g
⎛ ⎞ ⎜ ⎟ ⎝ ⎠
=
3 1
3 1
+
− ( ) 3 f
g
⎛ ⎞ ⎜ ⎟ ⎝ ⎠
=
4
2
= 2
Explanation:
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