Question

h(f(g(x))) where f(x)=4x+3, g(x)=-5x, h(x)=6-2x

Answer 1

h( f( g(x) ) ) = 6-2( 4 (-5x) + 3 )

Answer 2

why is it 6-2( 4(-5x)+3) and not 6-2( 4x(-5x)+3)?

Answer 3

Let's break this down step-by-step. I'm representing the functions only with their letter to clean it up a bit.

\[=6-2*f(g)\]
\[=6-2*(4(g)+3)\]
\[=6-2*(4(-5x)+3)\]
\[=6-8(-5x)+6\]
\[=6+40x+6\]
\[=40x+12\]

The actual x variable only enters the equation after the final substitution because neither h nor f is a function of x. Only g is.

Answer 4

aah! I get it now! Thank you so much!