Question

Given that the f(y) = y - 1 and g(y) = y^3 - 2y - 1, find (gof) (y)I and hence, (gof) (-6).

Answer 1

$(g \circ f)(y)=(y-1)^3-2(y-1)-1\\(g \circ f)(y)=y^3 - 3 y^2 + 3 y - 1-2y+2-1\\(g \circ f)(y)=y^3 - 3 y^2 +y\\\\(g \circ f)(-6)=(-6)^3-3\cdot(-6)^2+(-6)\\(g \circ f)(-6)=-216-108-6\\(g \circ f)(-6)=-330$