The option fourth is the answer after rationalization of the difference quotient.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
[tex]\rm g(x) = \sqrt{x}[/tex]
x > 0
Difference quotient:
[tex]= \rm \dfrac{f(x+h)-f(x)}{h}[/tex]
f(x+h) = √(x+h)
[tex]= \rm \dfrac{\sqrt{x+h}-\sqrt{x}}{h}[/tex]
[tex]= \rm \dfrac{\sqrt{x+h}-\sqrt{x}}{h}\times \dfrac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+\sqrt{x}}[/tex]
[tex]= \rm \dfrac{1}{\sqrt{x+h}+\sqrt{x}}[/tex]
Thus, the option fourth is the answer after rationalization of the difference quotient.
Learn more about the function here:
brainly.com/question/5245372
#SPJ1
