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

Just add the functions:

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

Combine:

-8x + 43. 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 + 134. 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

6x + 15. 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 + 26. If f(x) = 3x - 4 and g(x) = x + 2, find f - g

Subtraction:

3x - 4 - (x + 2)

3x - 4 - x - 2

2x - 67. 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

15x - 20 + 2

15x - 189. 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 - 210. 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

3x^2 + 2x - 811. 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)

3x - 1513. 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 5.8314. Find the distance between the two points (5, 1) and (8, 5)

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)

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

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.

3x - 4 + (x + 2)

4x - 2

Let me know if you have any more questions,

Ok, here goes:

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

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

= 52. Find the distance between the pair of points: (-2, -6) and (7, -3)

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,