Question

Given f(x)=4x+6 and g(x)=9x+9
then what is f(g(−6))?

Given f(x)=3x+8 and g(x)=6x+6
then what is (f+g)(−1))?

Given f(x)=3x+8 and g(x)=6x+6
then what is (f−g)(−1))?

Answer 1

\[f \left\{ g \left( x \right) \right\}=4 g \left( x \right)+6=4\left( 9x+9 \right)+6=36x+36+6=36x+42\]
now plug x=-6

Answer 2

\[f(g)\rightarrow f[g(x)]\]\[(f+g)(x)=f(x)+g(x)\]\[(f-g)(x)=f(x)-g(x)\]

Answer 3

Alternatively,
find \(g(−6)\) first
\[g(−6)=9(−6)+9=−45\],
and plug it into \(f\)
\[f(g(−6))=f(−45)=4(−45)+6\]

Answer 4

for the second part of the question
use: \[(f+g)(x)=f(x)+g(x)\]

and for the third part
use: \[(f-g)(x)=f(x)-g(x)\]