Evaluate (if possible) the function f(x)=1/x at the specified value of the independent variable and simplify the results

Question

(F(1+ΔX)-f(1))/Δx

Answer 1

I think the easiest way to start is to break the larger function into its pieces:

f(1+Δx) = 1/(1+Δx)

f(1) = 1/1 = 1

Then combine them, getting common denominators:

1/(1+Δx) - 1 = 1/(1+Δx) + (1+Δx)/(1+Δx) = (-Δx)/(1+Δx)

If we take this and divide by Δx, we get (-1)/(1+Δx)