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GREYUIT [131]
2 years ago
15

Given f(x) = log(x+1), x >-1 and g(x) = x^2 + 2x, XER find (f•g)(1)​

Mathematics
1 answer:
worty [1.4K]2 years ago
3 0

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

Step-by-step explanation:

did this Help?

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Y ≤ -2x + 4. What points satisfy the inequality?
MrRissso [65]
​Subtract 4 from both sides
y−4≤−2x

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-  y-4/2  ≥ x

 Switch sides
<span>x  ≤  −   y−4/2<span><span><span><span><span>​​</span></span></span>​​





HOPE THIS HELPS!!
</span></span></span>
6 0
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Morgarella [4.7K]

✽ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ✽

➷ 455+446= 901

✽

➶ Hope This Helps You!

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↬ May ♡

4 0
2 years ago
The coordinates of points A
Svetllana [295]

Answer:

Distance=13.60

Step-by-step explanation:

The Distance between the two points in coordinate system is find by using the distance formula.

If two points (x_1,y_1) and (x_2,y_2) are given:

Distance =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

For the points:

                     (-7, 5)\\ and \\(4, -3)

Distance=\sqrt{(4-(-7))^2+(-3-5)^2}\\\\ =\sqrt{(4+7)^2+(-8)^2} \\\\=\sqrt{11^2+(-8)^2} \\\\=\sqrt{121+64}\\\\ =\sqrt{185}\\\\ =13.60

The distance between the points is 13.60

7 0
3 years ago
I need help :) please if you know this I would appreciate it if you can help me
elena-14-01-66 [18.8K]

Step-by-step explanation:

a.

2(3x) - 5x = 4

6x - 5x = 4

x = 4

B. -5(x-4)+8x=29

-5x+20+8x=29

3x+20=29

3x=9

x=3

C. 2y=18+2(3-y)

2y=18+6-2y

2y=24-2y

4y=24

y=6

D. c = -b - 11

3c + 6 = 6b

3( -b - 11) +6 = 6b

-3b-33+6=6b

-3b-27=6b

-27=9b

3=b

3 0
2 years ago
In the number 9440 how many times greater is the 4 marked x more Han 4 marked y
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I dont even know what your asking 
4 0
3 years ago
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