Hello, i'm currently doing functions and I was fine until I got to multiplication. I really don't know what i'm doing, and would really appreciate a step by step on a few questions.
f(x) = -3x + 9
g(x) = 8x + 7
Find g(f(x))
I got -24x + 16.
Another :
f(x) = -3x + 9
g(x) = 8x + 7
Find f(g(x))
Thanks in advance.
no, one term was right, but your constant is wrong.
do it this way :
f(x) = -3x + 9
g(x) = 8x + 7
then g(f(x))
= g(-3x+9)
= 8(-3x+9) + 7
= -24x + 72 + 7
= -24x + 79
and f(g(x))
= f(8x+7)
= -3(8x+7) + 9
= -24x - 21 + 9
= -24x - 12
Thank you so much! I've been sitting here for hours. Only 4 to go. Thanks :)
2 down.
I'm having trouble here
f(x) = 4x + 2
h(x) = -7x - 5
Find f(h(x))
I tried doing it how it was done above, but i'm not getting an answer listed.
= f(-7x - 5)
= 4x(-7x-5)+ 2
= 28x^2-20+2
= 28x^2-18
Where am I going wrong :| ?
ALSO -
f(x) = 4x-3
g(x) = x2-2
Find f(3a-4)
from
= f(-7x - 5) to
= 4x(-7x-5)+ 2
you are replacing the x, so don't leave the x there.
should be
= 4(-7x-5)+ 2
= -28x - 20 + 2
= -28x - 18
for
f(x) = 4x-3
g(x) = x2-2
Find f(3a-4)
I will assume g(x) = x^2 - 2
then f(3a-4)
= 4(3a-4) - 3
= 12a - 16 - 3
= 12a - 19
the x in f(x) was merely replaced by 3a-4, so you have to replace it everywhere that you see an x.
No problem! I can walk you through these problems step by step.
First, let's start with the function g(f(x)).
To find g(f(x)), we need to substitute f(x) into the function g(x).
Start by replacing x in the function g(x) with the expression for f(x):
g(f(x)) = 8(f(x)) + 7
Next, substitute the expression for f(x) into g(f(x)):
g(f(x)) = 8(-3x + 9) + 7
Now, let's simplify the expression by distributing the 8 into the parentheses:
g(f(x)) = -24x + 72 + 7
Combine like terms:
g(f(x)) = -24x + 79
So, the answer to g(f(x)) is -24x + 79.
Now let's move on to the second question, which is finding f(g(x)).
Again, we need to substitute g(x) into the function f(x):
f(g(x)) = -3(g(x)) + 9
Substitute the expression for g(x) into f(g(x)):
f(g(x)) = -3(8x + 7) + 9
Distribute the -3 into the parentheses:
f(g(x)) = -24x - 21 + 9
Combine like terms:
f(g(x)) = -24x - 12
So, the answer to f(g(x)) is -24x - 12.
I hope this helps clarify the process for finding the composition of functions. Let me know if you have any more questions!