Question

f(x) = $x^3$ + x + 5
g(x) = $x^2$ + 9 + $\frac{1}{x}$
find fog/gof for x = 1?

• A. $\frac{9429}{407}$
• B. $\frac{8203}{347}$
• C. $\frac{1622}{104}$
• D. $\frac{5115}{213}$

Answer 1

The correct option is A $\frac{9429}{407}$

fog = f(g(x)) and gof = f(f(x))
for x = 1
f(1) = 7
g(1) = 11
so f(g(x)) at x = 1
= $(11{)}^3$ + (11) + 5
= 1347
So, g(f(x)) at x = 1
g(7) = 49 + 9 + $\frac{1}{7}$
$=\frac{407}{7}$
So, fog/gof $=\frac{1347}{\frac{407}{7}}=\frac{9429}{407}$