Question

F(y)=3y^2-y+1, f(g(y))=12y^4-62y^2+81 g(y) = ?

Answer 1

The composite function f(g(y)) is given by: f(g(y)) = 36y^4 - 186y^2 + 81 - y + 1

Given:

F(y) = 3y^2 - y + 1

g(y) = 12y^4 - 62y^2 + 81

We need to find the composite function f(g(y)).

f(g(y)) = F(g(y)) = F(12y^4 - 62y^2 + 81)

Now, we substitute g(y) into F(y):

f(g(y)) = 3(12y^4 - 62y^2 + 81) - y + 1

f(g(y)) = 36y^4 - 186y^2 + 81 - y + 1

So, the composite function f(g(y)) is given by:

f(g(y)) = 36y^4 - 186y^2 + 81 - y + 1

Complete question:

Find the composite function: F(y)=3y^2-y+1, f(g(y))=12y^4-62y^2+81 g(y) = ?