function composition

[typingken]

Ok Eliz did teach me this concept but I am confused yet again because I am not sure how to plug in x^2?

Given that f(x)=x^2 - 8 x and g(x)=x+ 2, calculate
(a) f\circ g(x)= f(g(x))= f(x+2)= x^2(x+2)-8x <-----is this correct? If so were do I go after that.

(b) g\circ f(x)= g(f(x))=g(x^2-8x)= x(x^2-8x)+2 = ???? now what?


(c) f\circ f(x)= f(f(x))= f(x^2-8x)=x^2(x^2-8x)-8x <-----is this correct? If so were do I go after that.

(d) g\circ g(x)= g(g(x))=g(x+2)=x(x+2)2= ???? now what?

 

[galactus]

For #1, insert g into f. Wherever you see an x in

the f function, put g there. Like so:

\(\displaystyle (f\circ{g})(x)=f(g(x))=(x+2)^{2}-8(x+2)\)

See?. Now simplify. Use the same technique on the others.

Okey-doke.

 

[moronatmath]

could you simplify that for me? Thats were I am getting stuck

 

[stapel]

could you simplify that for me?

So your class hasn't covered how to multiply polynomials...? They really should have done that first, before getting to function composition....

See if the following helps:

. . . . .FreeMathHelp lesson: Multiplying Polynomials

Once you've studied the basics of polynomial multiplication, please attempt the simplification. If you get stuck or are unsure of your answer, please reply showing your steps.

Thank you.

Eliz.