Learned, but then forgot: how do you solve for [f o g](x)?

[GetThroughDiffEq]

Just an example:

If f(x)=(x^4)-(20-x)

and

g(x)=(x^8-1)

solve for

[f o g](x)

and

[g of f](x)

 

[pka]

Just an example:

If f(x)=(x^4)-(20-x)

and

g(x)=(x^8-1)

solve for

[f o g](x)

and

[g of f](x)

\(\displaystyle f\circ g(x)=f(g(x))~\&~g\circ f(x)=g(f(x))\)

EXAMPLE \(\displaystyle a(x)=x^3+\sin(x)~\&~b(x)=2-|x|\)

then \(\displaystyle a\circ b(x)=(2-|x|)^3+\sin(2-|x|)\)

and \(\displaystyle b\circ a(x)=2-|x^3+\sin(x)|\)

 

[Otis]

f(x)=(x^4)-(20-x)

g(x)=(x^8-1)

solve for

[f o g](x)

Hello. Function [f◦g](x) is called a 'composite function' because it is a composition of two functions: The output from function g becomes the input to function f.

g(x) = x^8 - 1

Symbol x represents the input, and the expression x^8 - 1 represents the output.

f(x) = x^4 + x - 20

Symbol x represents the input, so how do we show the output of function g as the input to function f? By replacing each input symbol x with the expression x^8-1.

As pka's other example shows: [f◦g](x) = f(x^8 - 1)

?