Answer
Given $f(x)$ and $g(x)$
1. $(f o g)(x) = f(g(x))$
To find this, substitute the entire value of $g(x)$ for $x$ in $f(x)$. For instance, if
$f(x) = x^2$
and
$g(x) = 3x$,
$(f o g)(x) = f(g(x)) = f(3x) = (3x)^2 = 9x^2$
2. $(g o f)(x) = g(f(x))$
To find this, substitute the entire value of $f(x)$ for $x$ in $g(x)$. For instance, if
$f(x) = x^2$
and
$g(x) = 3x$,
$(g o f)(x) = g(f(x)) = g(x^2) = 3(x^2) = 3x^2$
Work Step by Step
Given $f(x)$ and $g(x)$
1. $(f o g)(x) = f(g(x))$
To find this, substitute the entire value of $g(x)$ for $x$ in $f(x)$. For instance, if
$f(x) = x^2$
and
$g(x) = 3x$,
$(f o g)(x) = f(g(x)) = f(3x) = (3x)^2 = 9x^2$
2. $(g o f)(x) = g(f(x))$
To find this, substitute the entire value of $f(x)$ for $x$ in $g(x)$. For instance, if
$f(x) = x^2$
and
$g(x) = 3x$,
$(g o f)(x) = g(f(x)) = g(x^2) = 3(x^2) = 3x^2$