Composition Equation

Question

If f(x)=2x^2+1 and g(x)=x-1 find (f o g)(x) - (g o f)(x) 

 

 

Answer 1

Whenever you have composition functions, you must put the whole function in instead of x.

For example, (f o g) (x) means f of g(x) so wherever you see "x" in the f(x) function, you put in the WHOLE g(x) function. As follows,

(f o g)(x)=2(x-1)^2+1

Then you simplify,

=2(x^2-2x+1)+1

=2x^2-4x+2+1

=2x^2-4x+3

 

Now, we do the same for g of f(x)

(g o f)(x)=2x^2+1-1

=2x^2

 

Now, we subtract our both results,

(2x^2-4x+3)-(2x^2)

=-4x+3