Question

Okay so just tried to do f(x) = -4x + 7 and g(x) = 10x - 6, find f(g(x)). And i got 5x-3 for my final answer. -Help please

Answer 1

Okay, \[f(x) = -4x+7\]\[g(x) = 10x -6\]You want \(f(g(x))\)

The way to think of this is as a recipe. Don't get confused the by fact that we recycle the letter \(x\)! It may be easier to think of this with different letters:

\[f(y) = -4y+7\]\[g(x) = 10x-6\]

\(g(x)\) is still \(10x-6\) but when we do \(f(g(x))\) we are doing \(f(y) = f(10x-6)\)
That means we take \[f(y) = -4y+7\]and replace \(y\) with \((10x-6)\):\[f(y) = f(g(x)) = -4(10x-6) + 7\]\[f(g(x)) = -4*10x -4*(-6) + 7 = -40x +31\]

Does that make sense to you?

Answer 2

im stuck after i times them by each other in paranthases

Answer 3

times what by each other?

Answer 4

You aren't multiplying the functions, you're substituting one function for the argument of the other.

Answer 5

i get -40x+24-70x-42

Answer 6

Look at my last two lines again:
\[f(y) = f(g(x)) = -4(10x-6)+7\]
\[f(g(x)) = -4*10x -4*(-6) + 7 = -40x + 24 + 7 = -40x +31\]

Answer 7

oh god thats confusing

Answer 8

then i just got 14=14...pellet

Answer 9

Look, \[f(x) = -4x+7\]is just a recipe. It says "take the thing you are given (we'll call it \(x\)), multiply it by -4, and add 7 to the result"

So when the thing it is given is the expression \(10x-6\), we multiply \((10x-6) \text{ by } -4\), giving us \(-4(10x-6) = -4*10x -4(-6) = -40x + 24\), and then we add 7 to the result, giving us \(-40x + 24 + 7 = -40x + 31\)

Answer 10

write out your steps for me, one step at a time, so I can point out where you are going astray...

Answer 11

now i got 40x-17

Answer 12

geeze

Answer 13

ok hold on

Answer 14

i do 4(10x-6)+7 which is 40x-24+7 which then i get 40x-17

Answer 15

No, it's not \(4(10x-6)+7\text{, it's }-4(10x-6)+7\)

\[f(x) = -4x+7\]

Answer 16

oh

Answer 17

Does that clear it up for you?