Question

f(x) = x2 – 9, g(x) = 2x + 3 and h(x) = x - 3. Find each of the following.
a) (f + g)(x)
b) (f/h)(x)
c) g(f(x))
d) f(g(h(x)))
e) (g – h)(8) f) h(f(-2))

Answer 1

all at once?

Answer 2

no

Answer 3

1) put a plus sign between them, combine like terms

Answer 4

2) put one on top of the other using a fraction bar

Answer 5

a)x^2 +2x-6. i think thats the answer to a)

Answer 6

c) requires some work
\[g(f(x))=g(x^2-9)=2(x^2-9)+3\] then distribute and combine like terms

Answer 7

you are right for A

Answer 8

the thing about b is that x-3 doesnt equal to zero,so the answer can't be 3.but when you do the whole x^2-9 thing the answer comes out 3.so that confuses me.

Answer 9

it does not come out to be 3
if you factor the numerator you get
\[\frac{x^2-9}{x-3}=\frac{x+3)(x-3)}{x-3}=x+3\] so long as \(x\) is not \(3\)
if \(x\) is 3, then the original expression is undefined

Answer 10

oh,so then it will be 3,awesome.

Answer 11

on c) i got 2x^2 -15,is it right?

Answer 12

yes

Answer 13

careful here
B is NOT 3, it is \(x+3\)

Answer 14

oh.
and c is correct?

Answer 15

yes

Answer 16

d came as 2x^2-18.