this is an example and I still cant figure it out!

[jjjppp]

For f(x) = 2x + 3 and g(x) = -x 2 + 1, find the composite function defined by (f o g)(x), there is no explanation as to how to solve.

 

[mmm4444bot]

g(x) = -x 2 + 1

I'm guessing that x 2 means x-squared; we type that as x^2.


there is no explanation as to how to solve

I'm thinking that this statement is completely false.

Have you seen any lessons on composite functions?

The notation f?g denotes a composition of functions f and g.

Specifically, the output of function g is used as the input to function f, to create the function f?g.

EG

f(x) = x^2 + 2x

g(x) = x/3

What is the composition f?g ?

In this example, the output of function g is x/3.

We use this output as the input to function f.

In other words, we determine f(x/3).

f(x/3) = (x/3)^2 + 2(x/3)

We see that f?g is x^2/9 + 2x/3.


Do you have a textbook? Look up "composite functions" or "functions, composite" in the index. If you cannot find definitions and examples for composite notation and functions, in your textbook, let us know.

Otherwise, please ask specific questions about the parts in your lessons that you do not understand.

Cheers ~ Mark