Composite functions!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Question

1)Given: f(x) = x^2, g(x) = x + 6, h(x) = 7 Find f{g[h(x)] }.

2)Find (f of g)(x) and (g of f)(x) for the indicated function
f(x)=7x-7, g(x)=x+7/7

(f of )(x)=?
(g off)(x)=?

 

Answer 1

1) The given fuctions f(x) = x^2 , g(x) = x+6, h(x) = 7

f {g[h(x)]} = f {g[7]}

               = f [ 7+6]

               = f (13)

f {g[h(x)]}  = (13)^2

f {g[h(x)]}  = 169

2) The given fuctions f(x) = 7x -7 and g(x) = (x+7)/7

(fof)(x) = f ( f (x))

          = f (7x -7)

          =  7 (7x - 7) - 7

          = 49x - 49 - 7

(fof)(x) = 49x - 56.

(gof)(x) = g( f (x))

           = g (7x - 7)

           = (7x - 7)+7/7

           = 7x/7  = x

(gof)(x) = x.