Question

given f(x)=2x^2-1 and g(x)=6-1/2x^2 find the following expressions


(g*f)(2) and (g*g)(0)

Answer 1

help

Answer 2

\[\large f(x)=2x^2-1,\quad g(x)=6-\frac{ 1 }{ 2 }x^2\] is this right?

Answer 3

yes

Answer 4

is that multiplication g * f or composition g of f?

Answer 5

g of f

Answer 6

both are compositions. (g of f)(2). sub x=2 in the expression in f(x). the answer you get, sub it in the expression in g.

Answer 7

g than has a circle f so that might be times right?

Answer 8

\[\large f(2)=2(2)^2-1=7\]use 7 in g(x)\[\large g(7)=6-\frac{ 1 }{ 2 }(7)^2=6-\frac{ 49 }{ 2 }=-\frac{ 37 }{ 2 }\]

Answer 9

if it's not a circle, then it is multiplication.