Question

help please! check out attachment in the comment box for the question

Answer 1

@plainntall do you know how to solve this?

Answer 2

f(x)=4x+1 and g(x)=x^2-5 and you need to find the composite function of f*g(4)

Answer 3

What does Composition Function mean?

Answer 4

so am I suppose to plug in the number 4 where x is

Answer 5

You can do that or put the second function g(x) in the first function f(x) and then solve it for 4. The key is that you put (x^2-5) into the f(x) function.where the x is.

Answer 6

okay thanks so much! im about to aatempt to solve

Answer 7

*attempt
I meant

Answer 8

so is it f(x) = 11?
@plainntall

Answer 9

If you do it by solve each function for x=4 first you have
g(4)=x^2-5 = (4)^2-5 = 16-5 = 11 so you got that part right, but this is a Composition function so you have to put the results of g(4) into f().
So f(g(4)=4(g(4))+1 which would be?

Answer 10

Remember g(4)=11

Answer 11

f(g) = 4g + 1/4?

Answer 12

@plainntall

Answer 13

The key here is that for a composition function the second function is put in where x appears for the first function.

Answer 14

that was the answer I got

Answer 15

That means for f*g(x) you put g(x)=x^2-5 into any place that f(x)=4x+1 appears.

That would look like f(x)=4(g(x))+1
=4(x^2-5) +1= 4x^2-20+1=4X^2-19
for x=4 that is?

You could also just solve g(x) for 4 which gets you the 11 which you plug into the f(x) equation which would be 4x+1=4(11)+1 = ?

Answer 16

It can be complicated but essentially you solve the second equation for the value of x then you put the results into the first equation to get the answer.

Answer 17

4x+1=4(11)+1 =
45!
so all i need to do now is plug in?

Answer 18

@plainntall

Answer 19

yes, 45 is correct

Answer 20

so thats the answer ?

Answer 21

I think the easiest way to think about it is when you have a function compostition f*g(x), solve for g(x) first then plug the results into the f(x) function.

Answer 22

yes the answer should be 45 since g(4)= 11 and f(11) = 45

Answer 23

thanks for taking your time with me.

Answer 24

Sure, I know this is complicated, but once you get it, it helps with everything that comes after.