Given:
f(x) = 5x² - x + 1
g(x) = -3x
Let's determine (f o g)(1),
(f o g)(1) = f(g(1))
Step 1: Let's determine g(1).
[tex]\text{ }g\mleft(x\mright)=-3x[/tex][tex]g\mleft(1\mright)=-3(1)\text{ = -3}[/tex]Step 2: Substitute g(1) as x in f(x).
[tex]f\mleft(x\mright)=5x^2-x+1[/tex][tex]\mleft(f\circ g\mright)\mleft(1\mright)=f\mleft(g\mleft(1\mright)\mright)=5(-3)^2\text{ - (-3) + 1}[/tex][tex]=5(9)\text{ + 3 + 1}[/tex][tex]=45\text{ + 4}[/tex][tex]\text{ }(f\circ g)(1)=\text{ 49}[/tex]Therefore, the answer is letter A. (f o g)(1) = 49
