Let f and g be functions from R to R defined by the followin

Let f and g be functions from R to R defined by the following formulas:
f (x) =1/(x2 + 2) , g(x) = 2x ? 1.
Find formulas for ( f ? g)(x) and (g ? f )(x)

5. Let L be the function defined in part 3 of Example 5.1.2 and let H be the function defined in exercise 4(a). Describe L o H and H o L 6. Letf and g be functions from R to R defined by the following formulas: x) =- r2 + 2, g(x) = 2x _ 1. Find formulas for (fog)(x) and (g o f)(x) 7. . suppose f : A B and C-A. The set/n (C x B ), which is a relation

Solution

a) ( f g)(x)= f(g(x))

   =1/((2x-1)^2 +2) =2+ 1/(2x-1)^2

b) (g f )(x)=g(f(x))

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