Answer
a/ f(2)=3*4-2+2=12
b/f(-2)=3*$(-2)^{2}$-(-2)+2 = 3*4+2+2 = 16
c/ f(a) = 3$a^{2}$-a+2
d/ f(-a) = 3$(-a)^{2}$-(-a)+2 = 3$a^{2}$+a+2
e/ f(a+1) = 3$(a+1)^{2}$-(a+1)+2 =3$(a+1)^{2}$-a+1
f/ 2f(a) = 2(3$a^{2}$-a+2) = 6$a^{2}$-2a+4
g/ f(2a) = 3$(2a)^{2}$-2a+2 = 12$a^{2}$-2a+2
h/ f($a^{2}$) = 3$($a^{2}$)^{2}$-$a^{2}$+2 = 3$a^{4}$-$a^{2}$+2
i/ $[f(a)]^{2}$ = (3$a^{2}$-a+2)^2
j/ f(a+h) = 3$(a+h)^{2}$-(a+h)+2 = 3$(a+h)^{2}$-a-h+2
Work Step by Step
f(x) =3$x^{2}$ - x + 2
x is the variable and by replacing x with a number, we can find the value of the function when x equals that number.
a/ f(2)=3*4-2+2=12
b/f(-2)=3*$(-2)^{2}$-(-2)+2 = 3*4+2+2 = 16
c/ f(a) = 3$a^{2}$-a+2
d/ f(-a) = 3$(-a)^{2}$-(-a)+2 = 3$a^{2}$+a+2
e/ f(a+1) = 3$(a+1)^{2}$-(a+1)+2 =3$(a+1)^{2}$-a+1
f/ 2f(a) = 2(3$a^{2}$-a+2) = 6$a^{2}$-2a+4
g/ f(2a) = 3$(2a)^{2}$-2a+2 = 12$a^{2}$-2a+2
h/ f($a^{2}$) = 3$(a^{2})^{2}$-$a^{2}$+2 = 3$a^{4}$-$a^{2}$+2
i/ $[f(a)]^{2}$ = (3$a^{2}-a+2)^2$
j/ f(a+h) = 3$(a+h)^{2}$-(a+h)+2 = 3$(a+h)^{2}$-a-h+2
