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Let f(x) = 9x - 2 and g(x) = -x + 3. Find f(g(x)).
-9x - 2
-9x + 5
-9x + 25
-9x + 27

- anonymous

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- ivettef365

just substitute the x on function f(x) for (-x+3)

- anonymous

Alright what do I do next?

- ivettef365

well you have
f(x) = 9x -2
9(-x+3) -2
= -9x + 27 -2
= -9x + 25

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## More answers

- anonymous

That makes so much sense!! Think that you can help me with another few?

- ivettef365

sure

- anonymous

Let f(x) = -4x + 7 and g(x) = 10x - 6, find f(g(x)).
-40x + 24
-40x + 31
-40x + 64
-40x + 70

- ivettef365

same process as previews problem
substitute the x from f(x) with (10x-6)

- anonymous

-40x + 64?

- ivettef365

how did you get to +64 ??

- ivettef365

you have
f(x) = -4x + 7
= -4(10x -6)+7
= -40x +24 + 7
= -40x + 31

- anonymous

Why would we not use that equation (-4x + 7) on the other side (g(x) = 10x - 6)?

- ivettef365

the question is f(g{x}), that means you are inserting g(x) inside the function f(x)

- ivettef365

if the question had been g(f{x}), then you insert f(x) inside g(x)

- anonymous

Oh okay, this is all making sense now, its all about reading the question properly!
Let f(x) = 12/4x + 2 Find f(-1).
-6
-2
2
6
How would I go about solving this?

- anonymous

@ivettef365 ?

- ivettef365

on his one just substitute the x from f(x) for -1

- ivettef365

so you have
12
---------
4x + 2

- ivettef365

solve as follows:
12
---------------
4(-1) + 2

- anonymous

6?

- anonymous

Since you've been helping me, this is all making so much sense now

- anonymous

Let f(x) = x + 8 and g(x) = x2 - 6x - 7. Find f(g(2)).
-7
-3
10
33
@ivettef365 ??

- anonymous

When there is the "2" In f(g(2)) what does that mean and how would I go about solving that?

- ivettef365

on the previews quetions you have 12 /-2 = -6
remember when dividing a positive with negative answer is negative

- ivettef365

I'm glad I can help

- ivettef365

on this problem,
f(x) = x + 8 and g(x) = x2 - 6x - 7. Find f(g(2)) first step substitute the x for 2 on g(x)
g(x) = x^2 - 6x -7
2^2 - 6(2) -7
4 -12-7
4 -19 = -15

- ivettef365

now you can substitute the x from f(x) for -15, try it to see if you get to answer

- anonymous

-7 right?

- anonymous

@ivettef365

- ivettef365

correct

- anonymous

Let f(x) = x - 2 and g(x) = x2 - 7x - 9. Find f(g(-1)).
-21
-3
3
21

- ivettef365

now you try doing it and I let you know if is correct.
first step substitute the x from g(x) for -1

- anonymous

I keep running into this problem, (-1)2 - 7(-1) - 9
-2 + 7 - 9 = 4
4 - 2 = 2 and that is none of the possible answers

- anonymous

0?

- ivettef365

sorry, my mistake now so (-1)^2 = 1
so you have 1 +7-9 = ??

- anonymous

-1!

- ivettef365

correct, now substitute the -1 for the x on f(x)

- anonymous

-3!

- ivettef365

correct, good job

- anonymous

Let f(x) = 2x + 2. Solve f^-1(x) when x = 4.
1
3
4
10
This one is confusing me because of the "f^1" how would I go about doing this and equations like this?

- anonymous

@ivettef365

- ivettef365

that is the inverse function

- ivettef365

sorry, erased it by mistake, here it is again, to find the inverse function
f(x) = 2x + 2 you need to write the function as follows:
x = 2y + 2
x-2 = 2y
x - 2
------- now substitute the x for the 4
2

- anonymous

1:)

- anonymous

Let f(x) = 2x - 6 Solve f-1(x) when x = 2.
-5
4
-2
7
Can you show me how I would re-write the inverse function to solve this one?

- anonymous

I was a little unclear about how to re-write it @ivettef365

- ivettef365

sorry, I went a little bit fast, because I am at work, and boss was calling me
but let me explain, the inverse of a function is just to isolate the x, so in order to do that you get the function f(x) = 2x + 2 and re-write it as
x = 2y + 2 ( I substitute the x for y, that way I isolate the y that is on my x value place)
x - 2 = 2y (I transfer the 2 to the other side, to transfer you have to change the sign)
x - 2
----- = y (now I divided by 2 on both sides, and the y stays by itself because
2 2y/2 = y) and there you have the inverse

- ivettef365

now try to do the inverse on this problem you have f(x) = 2x - 6
you write it as x = 2y - 6 (isolate the y)

- anonymous

x-6/2 = y?

- ivettef365

remember when you switch a number to the other side need to change the sign

- anonymous

x+6/2 = y then right?

- ivettef365

good job, now just substitute the x for 2 that is the easy part

- anonymous

4!:) Thank you so much for all of your help in teaching me these topics!

- ivettef365

your welcome :)

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