Given,
The expression is,
[tex]f(x)=6x^2+4x-1[/tex]Substituting x = 0,
[tex]f(0)=6(0)^2+4(0)-1=-1[/tex]The value of f(0) is -1.
Substituting x = 2,
[tex]f(2)=6(2)^2+4(2)-1=31[/tex]The value of f(2) is 31.
Substituting x = -2,
[tex]f(-2)=6(-2)^2+4(-2)-1=15[/tex]The value of f(-2) is 15.
Substituting x = x+1,
[tex]\begin{gathered} f(x+1)=6(x+1)^2+4(x+1)-1 \\ =6(x^2+1+2x)+4x+4-1 \\ =6x^2+6+12x+4x+3 \\ =6x^2+16x+9 \end{gathered}[/tex]The value of f(x+1) is 6x^2+16x+9.
Substituting x = -x,
[tex]\begin{gathered} f(-x)=6(-x)^2+4(-x)-1 \\ =6(x^2)-4x-1 \\ =6x^2-4x-1 \end{gathered}[/tex]The value of f(-x) is 6x^2-4x-1.
