I need help with this question: let g(x)=1-x^3

Question

find g(a) _____

find g(x)-g(a). simplify_____

find (g(x)-g(a))/(x-a). simplify_____

Answer 1

g(a) = 1-a^3

g(x) -g(a) = 1-x^3 -(1-a^3) = a^3 -x^3

(g(x)-g(a))/(x-a) = (a^3-x^3)/(x-a) = - (a^3-x^3)/(a-x)

= -(a-x)(a^2+ax+x^2)/(a-x)

= -(a^2+ax+x^2)

= -a^2 -ax-x^2