Question

Find all the values of x for which the function is differentiable. f(x)= (x^3-8)/(x^2-4x-5)

Answer 1

The function is differentiable for:
x² - 4 x - 5 ≠ 0
x² - 5 x + x - 5 ≠ 0
x ( x - 5 ) + ( x - 5 ) ≠ 0
( x - 5 ) ( x + 1 ) ≠ 0
x ≠ 5 and x ≠ - 1
Answer: x ∈ R \ { -1, 5 }