Question

MEDAL
f(x)=(x^2+3x-4) and g(x)=(x+4)
a) find FOG and state the domain
b) find f/g and state the domain.

Answer 1

@campbell_st @ganeshie8 @dan815 @Nnesha @wolf1728

Answer 2

HI!!

Answer 3

HI! Please help me!

Answer 4

\[f\circ g(x)=f(g(x))\] we work from the inside out

Answer 5

\[f(g(x))=f(x+4)\] is a start

Answer 6

Is for the first one x^2+11x+32 with the domain as all real numbers?

Answer 7

then since
\[f(\diamondsuit)=\diamondsuit ^2+3\diamondsuit-4\] you have
\[f(x+4)=(x+4)^2+3(x+4)-4\]

Answer 8

then algebra give me a sec
but the domain is all real numbers for sure

Answer 9

I mean +28 at the end

Answer 10

i get \((x+8) (x+3)\) or
\[x^2+11x+24\] same thing

Answer 11

Okay, and fr the second one?

Answer 12

oh hold on let me see about the constant again

Answer 13

24 is right

Answer 14

Okay and how do I do f/g

Answer 15

at the risk of sounding silly, put f over g

Answer 16

ok i copied that wrong it is
\[\frac{x^2+3x-4}{x+4}\] so the domain is all numbers except \(-4\)

Answer 17

now we can factor and cancel \[\frac{(x+4)(x-1)}{x+4}=x-1\]

Answer 18

Now what?

Answer 19

(x-1)/1 = (x-1)?

Answer 20

now go have a nice glass of wine
since we are done

Answer 21

So how would I write the solution?

Answer 22

y=x-1?

Answer 23

as \(x-1\) for \(x\neq -4\)

Answer 24

Thank you so much!

Answer 25

\[\color\magenta\heartsuit\]