Question 380901
{{{f(x) = 18/(x+4)}}}
{{{g(x) = root(3, x)}}}
a. (g of f)(2)
First let's find (g of f)(x):
(g of f)(x) = g(f(x)) = {{{g(18/(x+4)) = root(3, 18/(x+4))}}}
So (g of f)(2) = {{{root(3, 18/((2)+4)) = root(3, 18/6) = root(3, 3)}}}<br>
b. (f o f)(1)
Again, let;s tart with (f o f)(x):
(f o f)(x) = f(f(x)) = {{{f(18/(x+4)) = 18/((18/(x+4)) + 4)}}}
(f o f)(1) = {{{18/((18/((1)+4)) + 4) = 18/(18/5 + 4) = 18/(18/5 + 20/5) = 18/(38/5) = 18*(5/38) = 90/38 = 45/19}}}