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Scott, MIT Graduate
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1. Given f(x) 5x + 4 and g(x) 3x - 8 find ...

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1. Given f(x) = 5x + 4 and g(x) = 3x - 8: find f(dot)g

2. Given f(x) = 2 - 2x and g(x) = -6x + 2, find f + g

3. Given f(x) = -3x + 2 and g(x) = 2x + 9: find (gof)(x)

4. Given f(x) = 8x - 2 and g(x) = 2x - 3, find f - g

5. Given f(x) = 5x + 7 and g(x) = 5x - 1: find (fog)(x)

6. If f(x) = 3x - 4 and g(x) = x + 2, find f - g

7. Find the midpoint of the line between the two points (-2,-1) and (-8, 6)

8. If f(x) = 5x + 2 and g(x) = 3x - 4: find (fog)(x)

9. If f(x) = 2x^2 -x - 3 and g(x) = x + 1, find f + g

10. If f(x) = 3x - 4 and g(x) = x + 2: find f(dot)g

11. Find the midpoint of the line between the two points (10, 4) and (2, 6)

12. If f(x) = 3x and g(x) = x = 5: find (fog)(x)

13. Find the distance between the two points (0, 0) and (3, 5)

14. Find the distance between the two points (5, 1) and (8, 5)

15. If f(x) = 3x -4 and g(x) = x + 2, Find f + g

Hi, and welcome back to JA!

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1. Given f(x) = 5x + 4 and g(x) = 3x - 8: find f(dot)g

Dot means multiplication:

(5x+4)(3x-8)

Using FOIL:

15x^2 + 12x - 40x - 32

Combine like terms:

15x^2 - 28x - 32

2. Given f(x) = 2 - 2x and g(x) = -6x + 2, find f + g

Just add the functions:

2 - 2x + (-6x + 2)

Combine:

-8x + 4

3. Given f(x) = -3x + 2 and g(x) = 2x + 9: find (gof)(x)

With the "o" operator you plug the second function into the first:

2(-3x + 2) +9

-6x + 4 + 9

-6x + 13

4. Given f(x) = 8x - 2 and g(x) = 2x - 3, find f - g

Here, we just subtract:

8x - 2 - (2x - 3)

Distribute the minus sign:

8x - 2 - 2x + 3

Combine:

6x + 1

5. Given f(x) = 5x + 7 and g(x) = 5x - 1: find (fog)(x)

Plug g into f for x:

5(5x-1) + 7

Distribute:

25x - 5 + 7

25x + 2

6. If f(x) = 3x - 4 and g(x) = x + 2, find f - g

Subtraction:

3x - 4 - (x + 2)

Distribute:

3x - 4 - x - 2

Combine:

2x - 6

7. Find the midpoint of the line between the two points (-2,-1) and (-8, 6)

The midpoint will be at the point: (xavg,yavg)

((-2+-8)/2,(-1+6)/2)

(-5, 2.5)

8. If f(x) = 5x + 2 and g(x) = 3x - 4: find (fog)(x)

Plug g into f:

5(3x-4) + 2

Distribute:

15x - 20 + 2

Combine:

15x - 18

9. If f(x) = 2x^2 -x - 3 and g(x) = x + 1, find f + g

Add the functions:

2x^2 -x - 3 + (x + 1)

Combine like terms (cancel the x's):

2x^2 - 2

10. If f(x) = 3x - 4 and g(x) = x + 2: find f(dot)g

Multiply:

(3x-4)(x+2)

FOIL:

3x^2 - 4x + 6x - 8

Combine:

3x^2 + 2x - 8

11. Find the midpoint of the line between the two points (10, 4) and (2, 6)

Midpoint is the average of each x and y:

((10+2)/2,(4+6)/2)

(6, 5)

12. If f(x) = 3x and g(x) = x = 5: find (fog)(x)

Plug g into f.

I am assuming that g(x) = x - 5 (let me know if that's wrong)

3(x-5)

Distribute:

3x - 15

13. Find the distance between the two points (0, 0) and (3, 5)

Distance formula:

sqrt((x2-x1)^2 + (y2-y1)^2)

sqrt((3-0)^2 + (5-0)^2)

= about 5.83

14. Find the distance between the two points (5, 1) and (8, 5)

Distance formula:

sqrt((x2-x1)^2 + (y2-y1)^2)

sqrt((8-5)^2 + (5-1)^2)

= 5


15. If f(x) = 3x -4 and g(x) = x + 2, Find f + g

Add them:

3x - 5 + (x + 2)

Combine like terms:

4x - 3

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Wow! That took quite a while!

I hope this helps. Let me know if you have any questions,

Scott

Customer: replied 9 years ago.
Reply to Scott's Post: Scott, I have a question about your answers for question 14 and 15. I was given multiple choice answers and your answers don't match. Here are the choices. For question 14:

1. square root symbol over 85
2.   "     "     "     "   17
3.   "     "     "     "   54
4.   "     "     "     "   34

question 15:
1. 4x - 2
2. 4x
3. x + 4
4. 2x - 4

Hi again,

14 is correct, the answer is 5.

I think your choices are for 13.

My answer for question thirteen of 5.83 is equal to sqrt(34)... same thing, just a different way of writing it.

You're absolutely correct about 15; I made a typo when I was pasting the f(x) into my work.

15. If f(x) = 3x -4 and g(x) = x + 2, Find f + g

Add them:

3x - 4 + (x + 2)

Combine like terms:

4x - 2

Let me know if you have any more questions,

Scott

Customer: replied 9 years ago.
Scott, I have 3 more questions to ask.

Find the distance between the pair of points:
1. (-1, -4) and (-5, -7)

2. (-2, -6) and (7, -3)

3.Find the midpoint of the line segment with the given endpoints: (2, 1) and (6, 8)

Ok, here goes:

1. Find the distance between the pair of points: (-1, -4) and (-5, -7)

Distance formula:

sqrt((x2-x1)^2 + (y2-y1)^2)

sqrt((-5-(-1))^2 + (-7-(-4))^2)

= 5

2. Find the distance between the pair of points: (-2, -6) and (7, -3)

Distance formula:

sqrt((x2-x1)^2 + (y2-y1)^2)

sqrt((7-(-2))^2 + (-3-(-6))^2)

= 9.49 = sqrt(90)

3.Find the midpoint of the line segment with the given endpoints: (2, 1) and (6, 8)

take the averages:

((2+6)/2,(1+8)/2)

(4, 4.5)

Let me know if you have any questions,

Scott

Customer: replied 9 years ago.
Scott, on question 2 my choices are
1. 6
2. 72
3.72 sqrt symbol over 2
4. 3 "     "      " 10
what would sqrt (90) be?

And on quest. 3, can 4.5 be converted into 9/2?
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