Question

If f(x)=x + 2 and g(x)=x^2 - 4x, find:
f(g(-3))

Answer 1

Thats functions right

Answer 2

Yes

Answer 3

evaluate g(-3) first amd then put that in the place of x in f(x) and evaluate the function.

Answer 4

So this would be correct?\[-3^2-4(-3)\]

Answer 5

parenthesis around (-3)

Answer 6

Not quite.

\[g(x) = x^2-4x\]\[x=-3\]\[g(-3) = (-3)^2-4(-3) =\]
then whatever that works out to be, plug it in as \(x\) in \(f(x) = x+2\)

Answer 7

Then the final answer to that would be 5 after I take the 3 and plug it in for f(x)?

Answer 8

need to check your arithmetic.

Answer 9

what is -3 * -3?

Answer 10

-9?

Answer 11

then what is 3 * -3?

Answer 12

No, 9.

Answer 13

yeah, so that's \[(-3)^2-4(-3) = 9-(-12) = \]

Answer 14

21

Answer 15

right! so \(g(-3) = 21\)
now what does \(f(21)=\)

Answer 16

23 because the f(21) would be 21 + 2

Answer 17

excellent!
\[f(g(-3)) = f(21) = 23\]

Answer 18

Thank you so much!

Answer 19

it can be a bit confusing at first, because the \(x\) gets used over and over again and isn't necessarily the same value. think of the f(x) = <something> as a recipe...