Question

f(x)=2x+4, m(x)=x^3

Find f of m. I don't know the steps to do this it is all new to me can someone walk me through the steps?

Answer 1

f(x)=2x+4


f(m(x))=2(m(x))+4


f(m(x))=2(x^3)+4


f(m(x)) = 2x^3 + 4

Answer 2

The real point here is that f(x) = 2x+4 doesn't really mean anything about "x", it just means f(whatever you put in) is twice what you put in plus 4. So when you put in m(x), which is x^3, what you get out is twice x^3, plus 4, just like the previous responder showed algebraically.

Answer 3

Now it says I need to find the first three iterates of f o m given \[x {_{0}}\]=-1

Answer 4

Does it say that these functions are recursive?

Answer 5

no it doesn

Answer 6

hmm well that's what it looks like even though the notation is odd...

Answer 7

So now you substitute x=-1 in the equation-f(m(x))=2*x^3 +4 and get the corresponding value of f(x). that value will become the next x1. then sustitute that and do this 3 times.

Answer 8

Do I put \[f(m(-1)=2(m(-1)=4\]

Answer 9

ya

Answer 10

and I do that with all three steps

Answer 11

well yes....you see you can find iterates using any standard methods like newton raphson, bairstow,etc....they r all different formulae to get the corresponding iterates. refer those and substitute the x values 3 times.

Answer 12

so it looks like this
\[f(m(-1)=2(m(-1^3)=4\]

Answer 13

then i Plug these into the calculator and get an answer?
or am I totally confused?

Answer 14

yes that is the first value.....but u need to get 2 more x values...and then corresponding f(m(x)) values...what course r u doing...Numerical methods??

Answer 15

Pre-cal

Answer 16

Methods of conbining funtions iterations

Answer 17

oh ok. then follow these steps-
Use this formula- x1=x0-(f(x0)/f'(x0))
In this formula substitute x=-1 and get x1. then substitute that value of x1 as x0 again and then again. So now you have three values of x. Substitute those values to get f(m(x)).

Answer 18

if you r still confused wiki Newton Raphson technique

Answer 19

I haven't heard of that one yet.

Answer 20

so what i just did isn't correct

Answer 21

I think amrit is talking about something totally different. You need to input your value into f(m(x)), and once you get the output of that, use it as the input for f(m(x)) again, and then repeat a third time. In other words you're computing f(m(x)) and then f(m(f(m(x)))) and then f(m(f(m(f(m(x)))))).

Answer 22

wow

Answer 23

let me tell you the question .
first find f o m . Your answer will be an algebraic expression, not a number. Next find the first three interates of f o m given x0=-1.
m=(x)=x^3 f(x)=2x=4

Answer 24

m(x)=x^3

Answer 25

f(x)=2x=4