I've tried every way I could think of, but I can't seem to get it right. How do you find the value of g(f(a)) when g(x)= x^2-2 and f(x)=-2x+7 p.s. I know the answer is 4a^2-28a+47..but I want to work through the problem.
I've tried every way I could think of, but I can't seem to get it right. How do you find the value of g(f(a)) when g(x)= x^2-2 and f(x)=-2x+7 p.s. I know the answer is 4a^2-28a+47..but I want to work through the problem.
the formula Mathivadhana99 used above is the same one i used:
$\displaystyle (a+b)^2 = (a+b)(a+b) = (a)(a+b) + (b)(a+b)$
$\displaystyle = (a)(a) + (a)(b) + (b)(a) + (b)(b)$.
since multiplication of real numbers is commutative:
$\displaystyle (b)(a) = ba = ab = (a)(b)$. so, continuing, we get:
$\displaystyle = a^2 + ab + ba + b^2 = a^2 + ab + ab + b^2 = a^2 + (ab + ab) + b^2 = a^2 + 2ab + b^2$.
this is basic, and just uses the distributive law:
$\displaystyle a(b+c) = ab + ac; (a+b)c = ac + bc$ repeatedly.