Question

Determine f(a+h)-f(a)/h for f(x)=1-x^2 and simplify

Answer 1

The answer is :

`(f(a+h)-f(a))/(h)=-2a-h`

EXPLANATION :

From the problem, we have the function :

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

We need to find f(a + h) and f(a).

That will be :

`\begin{gathered} f(a+h)=1-(a+h)^2 \\ =1-a^2-2ah-h^2 \\ \\ f(a)=1-a^2 \end{gathered}`

Then plug in to the required functions :

`\begin{gathered} (f(a+h)-f(a))/(h)=((1-a^2-2ah-h^2)-(1-a^2))/(h) \\ =(-2ah-h^2)/(h) \\ =-2a-h \end{gathered}`