Question

Given that f(x) = 2x + 1 and g(x) = −5x + 2, solve for f(g(x)) when x = 3.

Answer 1

Okay. Do you know the properties/ how to plug these in accordingly?

Answer 2

no i dont understand

Answer 3

Okay I am going to try to explain this as well as i can.

f(g(x)) refers to you taking g(x) and plugging it into x for f(x)


g(f(x)) refers to you taking the value of f(x) and plugging it into x in the g(x) value.

Answer 4

So looking at your problem you are trying to solve for f(g(x)) which means

f(x) = 2 (-5x+2)

Realize that they give you your x value. Which is 3. Can you plug this in now and see what you get?

Answer 5

bu where does the 3 go?

Answer 6

It goes in for the x value youve just created. When you do f(g(x)) or g(f(x)) you replace the current x value from the originall f or g equation.

So, with this being said. You plug in the value according to how they want it and then you simplify. The value of x is 3.

f(x) = 2 (-5(3) + 2)

can you simplify it now?

Answer 7

oh that makes more sense. I thought it would be something like f(2x + 1(−5x + 2(3)) and i was so confused.


so f(x) = 2 (-5(3) + 2) would be f(x) = -26?

Answer 8

but the options are
−91

−33

−25

35

Answer 9

Okay so,

my steps were
f(g(x)) = 2(-5x + 2) +1
f(g(x)) = 2(-5(3) + 2)) + 1
f(g(x)) = 2 (-15+2) +1
Now order of operations.
f(g(x)) = 2(-13) +1
f(g(x)) = -26 + 1
f(g(x)) = -25

Answer 10

Do you see how I got this answer?

Answer 11

yes that makes so much sense now!! thank you so much!

Answer 12

do you think you could help me with some more...?

Answer 13

Yeah sure thing just post them (:

Answer 14

how do i find the inverse of f(x) = x2 − 9?

Answer 15

f(x) = 2x + 9
let y = 2x + 9

interchange x and y
x = 2y + 9

now make y the subject of the formula

x = 2y + 9
x - 9 = 2y
(x - 9)/2 = y

f‾¹(x) = (x - 9)/2

Answer 16

Do you need more of an explanation?

Answer 17

Also if youre seeing boxes refresh the page and they go away (:

Answer 18

oooo wait I read the problem wrong!!!

Answer 19

so you are pretty much switching x for y and solving for y?

Answer 20

these are the options

Answer 21

I am so sorry :(! Here this is better for the explanation .

f(x) = x^2-9
y=x^2-9
x= y^2 -9
+9 +9

x+9= y^2

Now take the square root of the question and you should get

sqrt.(x+9) = y

Answer 22

+/- by the way. forgot that (:

Answer 23

so answer a is correct

Answer 24

ooooh thank you!

Answer 25

No problem (: Any more you need help with?

Answer 26

yes!

Answer 27

ask away haha (:

Answer 28

Given the function f(x) = 2x - 5/3, which of the below expressions is correct

^^^thats 2x - 5 divided by 3

Answer 29

Like this you do, we have been given f(x)=2x-5/3

so you can take that as also, y=2x-5/3
shift the 3 to the other side and division changes to multiplication, 3y=2x-5
now shift 5 to the other side and -ve becomes +ve, 3y+5=2x,

divide both sides by 2, so you get, 3y+5/2=x

now you can also write x as f-1(y)=3y+5/2

I just made f(x) as y to make it easier, of course there are many ways to do it

At the last, you can change it back to f-1(x) and you will get the same ans as: 3x+5/2

or answer C

Answer 30

why does the f(x) gets changed into f^-1(x)?

Answer 31

Because youre essentially looking for the other form which is your inverse for (f^-1)(x)

Answer 32

so for this problem i switch x and y, solve for y and when i get the answer i change y by f^-1(x)?

Answer 33

wait. not solve. i meant get y alone

Answer 34

Well you could do it that way yes. BUT you could also do (this may be easier for you.)

f(x) = 2x-5/3
y = 2x-5/3
Multiply both sides by 3 to get rid of the denominator.

3y=2x-5
add 5 to both sides.

3y+5 = 2x

divide by 2
(3y+5)/2 = x

Now you can do your inverse property and simply switch x and y

y= (3x+5)/2

Answer 35

oh now i get it! i just did another problem like this and got the right answer!

Answer 36

AWESOME! You seem to be catching on (:

Answer 37

i have like 2 or 3 more problems that i need some help on..

Answer 38

Find the average rate of change for the given function from x = −1 to x = 2.

Answer 39

Im stuck i kinda dont remmeber this one lol. I may if I look up some of it. do you have any formulas I could maybe go off of?

Answer 40

one sec

Answer 41

okay (:

Answer 42

this is what the textbook gives me

Answer 43

Okay sorry on the wait one second (:

Answer 44

its ok :)

Answer 45

Okay so by looking at the graph you are meant to find your y coordinates that correspond to the x coordinates. can you tell me those (im walking you through step by step) (:

Answer 46

so would a y coordinate be 1?

Answer 47

uhm no. one of the coordinates would be -1 because you should look at when you see the line pass through either underneath. above or through the x coordinate.