Thread: f(x) and g(x), need to solve (fg)(x) and (gf)(x)

f(x) = cuberoot(x+1) and g(x) = cosx

how do I do this?



Here is the note I took in class:

Let f and g be two functions having the domain D. The product of f and g is that function which assigns to x is a subset of D the number f(x)g(x)

fg
x ----> (fg)(x) = f(x)g(x)

Did I copy this incorrectly? I thought (fg)(x) = f[g(x)] not f(x)g(x)

help! Thanks

Originally Posted by bloodyfinger

f(x) = cuberoot(x+1) and g(x) = cosx

how do I do this?



Here is the note I took in class:

Let f and g be two functions having the domain D. The product of f and g is that function which assigns to x is a subset of D the number f(x)g(x)

fg
x ----> (fg)(x) = f(x)g(x)

Did I copy this incorrectly? I thought (fg)(x) = f[g(x)] not f(x)g(x)

help! Thanks

Hi bloodyfinger,

Usage varies sometimes by textbook and author. When in doubt, ask for clarification.

My opinion...I would look at as the product

It should have been written as . This way the meaning is clear.

If they had intended to indicate the composition of functions, they would've used to mean

Oh shoot, my mistake. I didn't realize there was a difference between and .

The original question actually asks me to find and .

How do I do this if and

Originally Posted by bloodyfinger

Oh shoot, my mistake. I didn't realize there was a difference between and .

The original question actually asks me to find and .

How do I do this if and

you do

Originally Posted by skeeter

you do

Is there any way to simplify or ?

Originally Posted by bloodyfinger

Is there any way to simplify or ?

looks like both are in "simple" form to me.

Originally Posted by skeeter

looks like both are in "simple" form to me.

That was shockingly easy.... I have a hard time believing the question was that simple... haha

Thanks so much though!!