1. f(g(x)) = y = (x+4)^2 + 3 = x^2 + 8x + 19
dy/dx = 2x + 8
2x + 8 = 0, x = -4
f(g(-4)) = 16 - 32 + 19 = 19 - 16 = 3
So the range is f(g(x)) >= 3
Anyone,
If you could help me with several questions that I have. They are as follows:
1) What is the range of (fog)(x) if f(x) = x(squared) + 3 and g(x) = x+4
2) What is g(x) =f-1(x) (the one is supposed to be for inverse not a negative number) if f(x) = 1/2x
3) Consider g(x) =(x+2)(cubed) + 3; what is the new equation for g(x) if it is shifted up 6 units and shifted right nine units
4) What is the range of (fog)(x) if f(x) = x(squared) + 3 and g(x) = x+4
5) What is f(x) if f(x) = z(x) +2 and z(x) = 2x-3
Any Help on these questions would be most appreciated.