Question

Let f(x) = x - 2 and g(x) = x2 - 7x - 9.

Find f(g(-1))

Answer 1

First find g(-1)

\[\large g(x) = x^2 - 7x - 9\]


\[\large g(-1) = (-1)^2 - 7(-1) - 9\]


\[\large g(-1) = 1 - 7(-1) - 9\]


\[\large g(-1) = 1 + 7 - 9\]


\[\large g(-1) = 8 - 9\]


\[\large g(-1) = -1\]

Answer 2

then you use this value of g(-1) to find f(g(-1))


f(x) = x - 2

f(g(-1)) = g(-1) - 2 ... replace each x with g(-1)

f(g(-1)) = -1 - 2 ... replace g(-1) on the right side with -1 (since g(-1) = -1)

f(g(-1)) = -3

Answer 3

coincidentally, g(-1) = -1, but the input and output are usually not the same

Answer 4

so f(g(-1)) = -3? im starting to understand this lesson

Answer 5

yes correct

Answer 6

i understood everything till f(x) came in the equation lol but thank you! im starting to understand it more

Answer 7

well you start with f(x) = x-2

then you replace x with g(-1) since you want f(g(-1))

Answer 8

so that explains how we got f(g(-1)) = g(-1) - 2

then on the right side you replace g(-1) with -1 because above we've shown that g(-1) = -1

Answer 9

OHHHHHHHHHHHH I see

Answer 10

glad it's clicking now

Answer 11

is easy. its just that if you think it too much it gets confusing

Answer 12

thank you!

Answer 13

yeah just take it one step at a time and you'll be fine

Answer 14

i know! thank you! but what about ? Let f(x) = x + 8 and g(x) = x2 - 6x - 7. Find f(g(2)) @jim_thompson5910

Answer 15

what is g(2)?

Answer 16

g(2) = x2 -6x - 7

g(2) = 2^2 - 6x - 7

???

Answer 17

@jim_thompson5910

Answer 18

you need to replace the x in -6x as well

Answer 19

g(x) = x^2 - 6x - 7

g(2) = (2)^2 - 6(2) - 7

g(2) = ???

Answer 20

yes yes i know that i forgot to type it in tho lol. g(2) = -15?

Answer 21

good

Answer 22

now that you know that g(2) = -15, you basically plug -15 into f(x) and evaluate

Answer 23

im learning better than in class lol. ok let me work that out

Answer 24

this is because f(g(2)) = f(-15) effectively since g(2) = -15

Answer 25

that's great you are

Answer 26

so....

f(x) = x + 8

f(-15) = -15 + 8

f(-15) = -7?

Answer 27

correct

Answer 28

so that means f(g(2)) = -7

Answer 29

wait so the final answer is f(g(2)) = -7? THANK YOU

Answer 30

yep, it is

Answer 31

thank you!

Answer 32

yw