Question

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

-9x - 2
-9x + 5
-9x + 25
-9x + 27

Answer 1

Start with f(x) = 9x - 2 and replace every x with g(x)

Answer 2

so,

f(x) = 9x - 2

f(g(x)) = 9(g(x)) - 2

Answer 3

since we have f(g(x)) = 9(g(x)) - 2 and because g(x) = -x+3, we know that

f(g(x)) = 9(g(x)) - 2

f(g(x)) = 9(-x+3 ) - 2... replace g(x) with -x+3

I'll let you simplify

Answer 4

im getting B @jim_thompson5910

Answer 5

9(-x+3 ) - 2 = 9(-x)+9(3 ) - 2

9(-x+3 ) - 2 = -9x + 27 - 2

9(-x+3 ) - 2 = ???

Answer 6

Im lost what to do after this point i keep getting 6 but that now a choice

Answer 7

do you see how I got -9x + 27 - 2

Answer 8

yes

Answer 9

so you just need to simplify -9x + 27 - 2

Answer 10

by combining like terms

Answer 11

so combine the -9x right?

Answer 12

nope, the 27 and -2 are like terms

Answer 13

the only like terms

Answer 14

So then it would be -9x+25

Answer 15

correct

Answer 16

can you help me with one more? @jim_thompson5910

Answer 17

sure, one more

Answer 18

Let f(x) = -4x + 7 and g(x) = 10x - 6. Find f(g(x)).

-40x + 24
-40x + 31
-40x + 64
-40x + 70

Answer 19

same idea as last time

Answer 20

I tried doing the same thing as the last one and got -4x+-17

Answer 21

f(x) = -4x + 7

f(g(x)) = -4(g(x)) + 7 ... replace every x with g(x)

f(g(x)) = -4(10x - 6) + 7 ... replace the g(x)'s on the right side with 10x-6

f(g(x)) = -4(10x) - 4(-6) + 7

f(g(x)) = -40x + 24 + 7 \(\Large \leftarrow \text{see note below}\)

f(g(x)) = -40x + 31


Note: this is where you made a mistake. Notice how the -4 outside multiplies with the -6 to get +24 and NOT -24.

Answer 22

Thanks !

Answer 23

you're welcome