Question

Given that f(x) = 2x + 1 and g(x) = −5x + 2, solve for f(g(x)) when x = 3

Answer 1

unfortunately, function notation isn't all it could be.

think of it like this:

\[f(x) = 2(x) + 1\] so whatever goes into the parentheses on the left goes into the parentheses on the right, too.

so \[f \left( g \left( x \right) \right)=2\left[ g \left( x \right) \right]+1=2\left[ -5(x)+2 \right]+1=\left[ -10(x) +4 \right]+1=-10(x) +5\] i used square brakets so you could see which was the input for f vs. the input for g.

Answer 2

now just plug in 3 for x and evaluate.
\[f \left( g \left( 3 \right) \right)=-10(3)+5\]