Question

Need help with functions and someone to check my answer for 3c. Lab is attached

Answer 1

@ranga

Answer 2

You may want to redo 3b and 3c.
3b) (f o g)(-1) = f(g(-1))
From the graph, g(-1) = ?
Then put what you find in f(?) and evaluate f(?)

Answer 3

(f o g)(-1)
2x+3
2(x^2+4x)+3
2(-1)^2+4(-1)+3
=-3

Where am I messing up?

Answer 4

How did you get g(x) = x^2+4x?

Answer 5

someone helped me

http://openstudy.com/study#/updates/53642800e4b0fac5fcff60dd

Answer 6

How did you go from line 2 to line 3 above?
You are putting x^2 + 4x in the place of x which implies g(x) = x^2 + 4x. How?

Answer 7

Will you please explain to me how to get g(x)? I am lost and keep getting different answers

Answer 8

Instead of giving you g(x) as a function they have provided you with a GRAPH. All you have to do is read the g(x) values from the graph.

Here they are asking you for (f o g)(-1)
which means find: f(g(-1)).
Since they have not given you g(x) as a function you need to find g(-1) from the graph.
When x = -1, what does the graph indicate g(-1) is?

Answer 9

3?

Answer 10

Yes. f(g(-1)) = f(3) = ?
f(x) = 2x + 3
f(3) = ?

Answer 11

9?

Answer 12

yes.

Answer 13

and 4 for c?

Answer 14

yes!

Answer 15

Geez! why did this have to take me so long i was making it way harder than it needed to be. Will you work thru the last few with me? is part g) (-4,2)?

Answer 16

If you draw a horizontal line at y (or g(x)) = 2, you will notice it intersects the graph at 3 points. So you will have to find all three points. You have correctly found the left most point. There are two more.

Answer 17

(-1,2)?

Answer 18

-1 looks closer to (-1,3)

Answer 19

true! and (-2,4)?

Answer 20

(-2,4) is the vertex of the parabola but that is not asked. We are looking for (?, 2). That is all three x-values that will make y = 2.

Answer 21

2?

Answer 22

-3

Answer 23

Yes, you have the correct rightmost point: (2,2).
The leftmost point is not correct (earlier I said it was but I notice at x = -4 a vertical line upwards will not intersect the graph. The point is approximately midway between -3 and -4 or about -3.5 and midway between 0 and -1 or -0.5.

Does the teacher want estimate from reading the graph or are they expecting you to figure out the equation of the parabola and given an accurate answer instead of an estimate from the graph?

Answer 24

I would assume an accurate answer she didn't specify. Real quick is e) 11?

Answer 25

yes 11 for e.

Answer 26

Can you explain how I do d? sorry!

Answer 27

d) fg(-2) = f(-2) * g(-2)
f(x) = 2x + 3
f(-2) = 2(-2) + 3 = -4 + 3 = -1

g(-2) = 4 (from the graph)

f(-2) * g(-2) = -1 * 4 = -4

Answer 28

Got it! thank you so so much for your help the way you explain everything really helps!

Answer 29

You are welcome.

For g) if you want to figure out the equation of the parabola to find the accurate value of x where g(x) = 2, then:

the vertex of the parabola is at (-2,4)
The equation of a parabola in the vertex form is: y = a(x-h)^2 + k where (h,k) is the vertex. So y = a(x- -2)^2 + 4 = a(x+2)^2 + 4
Here this is an upside down parabola and so a = -1
so y = g(x) = -(x+2)^2 + 4

Put g(x) = 2 and solve for x. You will get two values of x.

Then on the right hand side it is a straight line and so g(x) = 2 when x = 2 and so the point is (2,2).

Total 3 points where g(x) = 2.

Answer 30

Awesome! do you mind if we work thru f) real quick just so I'm sure

Answer 31

f or g?

Answer 32

f) (g+f)(2)

Answer 33

(g+f)(2) = g(2) + f(2)
g(2) = 2 (from the graph)
f(x) = 2x+3
f(2) = 2(2) + 3 = 7
g(2) + f(2) = 2 + 7 = 9.

Answer 34

Can I bug you with checking something and I promise thats it!

Answer 35

go ahead. if it is a short one I can do b4 logging off.

Answer 36

Just glancing over the two graphs to see if they are done correct?

Answer 37

8b) When specifying the range, the lower number should be on the left and the higher number on the right.

Answer 38

same with e?

Answer 39

same with d) and e).
c) looks correct.

Answer 40

Thank you so much you seriously saved me or I would have been way off on my functions!

Answer 41

You are welcome.

The Domain of f(x) will be the Range of the inverse function f^-1(x).
The Range of f(x) will be the Domain of the inverse function f^-1(x).

Answer 42

Good to know, you're awesome!