Question

For the given functions f and g, find the indicated composition

Answer 1

$(g\circ f)(x)\text{ means put f(x) in g(x)}$

That means replace x in g by f

f(x) = -4x + 7

g(x) = 3x + 9

Substitute x in g(x) by f(x)

$(g\circ f)(x)=3(-4x+7)+9$

Now let us simplify it

$(g\circ f)(x)=3(-4x)+3(7)+9=-12x+21+9$

Let us add the like terms 21 and 9

$(g\circ f)(x)=-12x+(21+9)=-12x+30$