Question

Find the domain and range of the function.

h(x)= - (square root of x+3)

Answer 1

f(x) = √(x-3)

f(x+h) = √(x+h-3)

f(x+h) - f(x) = √(x+h-3) - √(x-3)

[ f(x+h) - f(x) ] /h = [√(x+h-3) - √(x-3)]/h

multiply top and bottom with [√(x+h-3) + √(x-3)]

[ f(x+h) - f(x) ] /h = [(x+h-3) - (x-3)]/h[√(x+h-3) + √(x-3)]

= [ h /h[√(x+h-3) + √(x-3)]

= [ 1 /[√(x+h-3) + √(x-3)]

when h--> 0

derivative of √(x-3 = 1 / [√(x-3) + √(x-3)]

= 1/(2√(x-3))

Answer 2

so thats the domain and the range?