Question

Suppose that the functions f and g are defined for all real numbers x as follows.
f(x) = x + 2
g(x) = 4x + 3

Write the expressions for (f+g)(x) and (f-g)(x) and evaluate (f*g)(1).

Answer 1

Any idea how to start?

Answer 2

I am not really sure, I kind of just need someone to walk me through this problem. I am having a hard time with it

Answer 3

Ok so have you done any so far?

Answer 4

yes

Answer 5

Ok please post what you have done.

Answer 6

Oh you meant on this problem?

Answer 7

Yes

Answer 8

I haven't done anything on this problem. Sorry for the confusion

Answer 9

Ok so here is what we are looking at.

Answer 10

So, x+2 + 4x + 3

Answer 11

We need to combine like terms!

Answer 12

4x^2 + 5 ?

Answer 13

So combine the x and the constants.

Answer 14

Not quite look at 4x^2 again you are going to add one.

Answer 15

Is it 4x^3 or add one to four

Answer 16

Add one to the four

Answer 17

So it will become 5x.

Answer 18

Can we combine our constants?

Answer 19

That would be 5 as well

Answer 20

Yes so our answer is 5x + 5 would you like to try the other one?

Answer 21

And that's the expression right?

Answer 22

We still have another one to solve for.

Answer 23

Okay

Answer 24

So x + 2 = 4x + 3

Answer 25

Do we have to change the addition signs or does it stay the same?

Answer 26

All of the ones in the second will be minus.

Answer 27

x - 2 - 4x -3?

Answer 28

I think I might have said it a little confusingly.

Answer 29

So now we need to combine like terms.

Answer 30

-3x?

Answer 31

for the x terms?

Answer 32

Yes that is correct

Answer 33

Now for the constants?

Answer 34

2-3 = -1

Answer 35

so -3x -1

Answer 36

Correct!

Answer 37

So we actually have one more thing to solve for.

Answer 38

Sorry didn't notice until now.

Answer 39

great! okay so the next one

Answer 40

Ok so

Answer 41

Here is what we are looking at what is the one where the x usually is?

Answer 42

So what will we do with the 1?

Answer 43

we multiply?

Answer 44

No we will use that instead of the x in (f)x

Answer 45

Sorry f(x)

Answer 46

so f(1) = (4(1) + 3) * g(1) = (1 +2)

Answer 47

g(1) = 8?

Answer 48

or is it 7?

Answer 49

and then 7*3 = 21

Answer 50

With PEMDAS it would be what?

Answer 51

Now we need to substitute it into the equation.

Answer 52

Well I 4(1) + 3, which is 4(1) = 4 and then 4 +3 is 7?

Answer 53

Correct!

Answer 54

so the answer is 21 right?

Answer 55

3*7 = 21

Answer 56

Is that right?

Answer 57

Yes!

Answer 58

Thanks! Do you think you might be able to help me with one more question?

Answer 59

Sure!

Answer 60

By the way great job!

Answer 61

Thank you! hold on one sec, I have to draw it out

Answer 62

https://www.aleks.com/aleks/gif/student/pcalc752_3_2_2_2.png

Answer 63

can you open this?

Answer 64

try this one, sorry http://imgur.com/uByaXDx

Answer 65

@jchick

Answer 66

Sorry I didn't get a reply for a few min so I left the page I will look.

Answer 67

Okay!

Answer 68

I see the graph but where is the question?

Answer 69

I am going to type it now!
Use the graph of the function f below to find the following.

All values at which f has a local minimum
All local minimum values of f

If there is more than one answer, separate them with commas

Answer 70

@jchick

Answer 71

Ok sorry my computer wasn't letting me type anything.

Answer 72

Ok so they are looking for x. They want you to find the f(x).

Answer 73

SO how do I do that?

Answer 74

Hang on I am drawing a blank here.

Answer 75

This is what the question is looking for, all values at which f has a local minimum. do you think you can help me solve that first?

Answer 76

I believe that your local minimum is -3

Answer 77

You can find the local minimum by looking to see where the second to lowest point on the graph is.

Answer 78

Ok so your right it's -3?

Answer 79

what about the second question? how would i find that?

Answer 80

all local minimum values of f?

Answer 81

What second equation?

Answer 82

Ok

Answer 83

I do not see F mentioned anywhere in your graph.

Answer 84

Oh wait I see it is a graph of F

Answer 85

You have an absolute minimum but I didn't know you could have more than one local minimum.

Answer 86

Yeah this question confuses me :/

Answer 87

Hang on let me look at another resource.

Answer 88

Okay