Question

G(n-7) if g(x) =x^2-5/3x

Answer 1

Instead of x, we write n - 7 in the function equation

$g(x)=x^2-\dfrac{5}{3}x\\\\g(n-7)=(n-7)^2-\dfrac{5}{3}(n-7)\\\\\text{use} (a-b)^2=a^2-2ab+b^2\\\text{and distributive property}\\\\=n^2-2(n)(7)+7^2+\left(-\dfrac{5}{3}\right)(n)+\left(-\dfrac{5}{3}\right)(-7)\\\\=n^2-14n+49-\dfrac{5}{3}n+\dfrac{35}{3}\\\\\text{combine like terms}\\\\=n^2+\left(-14n-1\dfrac{2}{3}n\right)+\left(49+11\dfrac{2}{3}\right)\\\\=n^2-15\dfrac{2}{3}n+60\dfrac{2}{3}$