Question

For f(x)=3x+1 and g(x)=x²-6, find (f o g)(4)

Answer 1

well, (f o g)(4) is just another way of saying f( g(4) ).

so, we can simply first find g(4), and then plug that in f(x),


`\bf \begin{cases} f(x)&=3x+1\\ g(x)&=x^2-6\\ (f\circ g)(4)&=f(~~g(4)~~) \end{cases} \\\\\\ g(4)=(4)^2-6\implies g(4)=16-6\implies g(4)=10 \\\\\\ f(~~g(4)~~)\implies f(~~10~~)=3(10)+1\implies f(~~10~~)=31`