Question

Given the functions f (x) = x +1 and
g(x) = 3x − 2x^2 , find: f (f (-3))

Answer 1

-2

Answer 2

f (f (-3))

this means you first find f(-3)... which means you need to plug -3 in place of x into: x +1

Whatever that is equal to, you will plug that number into x+1 again.

The result of that is f(f(-3))

Answer 3

I got -2

Answer 4

Show your work.

Answer 5

f(-3) = -3 +1

then you still have to plug that again into x+1

Answer 6

f (x) = x +1 = f(x)=(-3+1)= -2
-2+1 = -1

Answer 7

Good job.

Answer 8

okay thanks so I have to solve and then plug back in

Answer 9

Yes, f(-3) is -2.

f(f(-3)) is thus the same as f(-2)

and f(-2) = -2 + 1.

Answer 10

if I have: Given the functions
f(x)=2x/x+5
and g(x)= 7-x/x-1
and I have to find f (g (3))

I plug into - 7-3/3-1 = 4/2 = 2

and then plug 2 back into 7-2/2-1 = 5/1 ?

Answer 11

no ... that's not right

Answer 12

You're on the right track. For f( g(3) ) - This time find g(3), which you've done. Now plug that number into f(x).

Answer 13

f(x) = -(4/3)

Answer 14

if f(x)=2x/x+5 where did you get -4/3 from?

f( g(3) ) means f(2), since g(3) = 2 as you found.

Answer 15

oh! g(x)=4/7

Answer 16

Excellent.

Answer 17

so if it asks me for f(g) I plug that into f(x) for x and then that answer I plug it into g(x) for x and vice versa. =)

Answer 18

Yep, basically you just start from inside the brackets, and move towards the outside

eg for a more complex example,

f( g( f(3) ) ) -start from the very inside part

for that, you'd first find f(3).

Then plug that number into g(x).

Then plug that number into f(x).

Answer 19

(a) f (g(1)) (b) g( f (1))
(c) f (g(x)) (d) g( f (x))
(e) f ( f (1)) (f) g(g(1))
(g) f ( f (x)) (h) g(g(x))

what does the f(f(x)) mean and the same for the g(g(x)) ?


I understand f(g) but not f(f)

Answer 20

Always just start from the inside, doesn't matter the letters, same process.

f( f(3) ) means find f(3) then plug that result into f.

g (g-2) ) means find g(-2) and plug that back into g.

Answer 21

ok thanks =)

Answer 22

one more questions?

Answer 23

sure

Answer 24

Oh sorry i misread you above.

f( f(x) ) means you have to plug the whole thing in, in place of x.

If f(x) = 2x + 3

then f( f(x) ) is

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

^see, just replace the x, with the actual function 2x+3

Answer 25

lets say this is my problem:Given the functions f (x) = x^2 + 2 and
g(x) = 5x −8 , find:
(a) f (g(1))
(c) f (g(x))
(e) f ( f (1))
(g) f ( f (x))
I understand the f(g(1)) - plug that into f(x) and the answer I get from that plug it into g(x). Would I plug the f(f(1)) into f(x) again even though I did that for A already?A

Answer 26

f( g(1) ) means find g(1) and plug that into f(x)

f( f(1) ) means find f(1) and plug that into f(x)

Answer 27

f ( g(x) ) means you need to plug the whole g(x), which is (5x −8) in place of x into f(x)

Answer 28

would I take that answer and put it back into g(x)?

Answer 29

Which?

Answer 30

f(g(x) plug (5x-8) in place of x into f(x)

Answer 31

Yes.