Question

f(x)=4x-3 and g(x)=x^2+1

find (fg)(x) and find and simplify g(x+h)-g(x)

Answer 1

That's \((fg)(x)\), not \((f \circ g)(x)\), right? If so, you just multiply, so \((fg)(x)=(4x-3)(x^2+1)\). As for the second part, plug in x+h for x in g(x), then subtract g(x).

Answer 2

its the second one...i thought they were the same...

Answer 3

Nope, two different things. \((f\circ g)(x)\) is the composition of the functions, also can be written as \(f(g(x))\). So, you plug g(x) in for the x in f(x).

Answer 4

so it should be 4x^2+1

Answer 5

When you substitute it in, don't forget to put parentheses around it. Also, don't forget the -3 :)

Answer 6

thanks! last quesion where do i get the h for the second part

Answer 7

You just use x+h, you don't need h to actually be anything. So just put (x+h) in instead of x, and then simplify it