Let fx 2x x2 Evaluate fx h fxh If fx x2 4x2 1 and gx

Let f(x) = 2x - x^2. Evaluate f(x + h) - f(x)/h. If f(x) = x^2 - 4/x^2 - 1 and g(x) = squareroot 2x - 3, find (f compositefunction g)(x). If f(x) = 4 - x/3x - 1, find the inverse of f and the domain and range of both f and f^-1.

Solution

f(x) = 2x - x^2

f(x+h) = 2(x+h) - (x +h)^2 = 2x +2h - x^2 - h^2 - 2xh

[ f(x+h) - f(x)]/h = ( 2x +2h - x^2 - h^2 - 2xh - 2x +x^2)/h

= (2h - h^2 -2xh)/h

= 2 - h -2x