Evaluate the difference quotient f3 h f3h h notequalto 0 i

Evaluate the difference quotient f(-3 + h) - f(-3)/h, h notequalto 0 if f(x) =1 -x -x^2. Find the inverse of the function y = Squareroot e^x +8 algebraically.

Solution

f(x) = 1 -x - x^2

f(-3+h) = 1 - (-3+h) - (-3+h)^2

= 1 + 3 - h - (h^2 - 6h + 9 )

=   - h^2 + 5h -5

f(-3) = 1 - (-3) - (-3)^2

= 1 + 3 - 9

= -5

f(-3+h) - f(-3) / h

= - h^2 + 5h -5 - (-5) / h

= -h^2 + 5h / h

= - h + 5