Given the functions f(x)= -x^2-2x-2, g(x)=2(x-2)+1 Find the following (simplify answers as much as possible.
a) g(f(x))
b) gf(1)
c) f(x+h)-f(x)/h
d) inverse of (g-1)(x)
a) g(f(x))
b) gf(1)
c) f(x+h)-f(x)/h
d) inverse of (g-1)(x)
-
g(f(x)
=2[(-x^2-2x-2)-2]+1
=2(-x^2-2x-4)+1
=-2x^2-4x-8+1
=-2x^2-4x-7
g(f(1))
-2(1)^2-4(1)-7
-2(1)-4-7
-2-4-7
-13
=2[(-x^2-2x-2)-2]+1
=2(-x^2-2x-4)+1
=-2x^2-4x-8+1
=-2x^2-4x-7
g(f(1))
-2(1)^2-4(1)-7
-2(1)-4-7
-2-4-7
-13