Question

Find the domain of the function f(x) = e^{(x/2 – 1)}  + log(1 – x) + x¹⁰⁰¹

Answer 1

Here, e^{(x/2 –1)}  is defined for all x in R log(1 – x) is defined for 1 – x > 0

⇒ x < 1 ⇒ x ∈ (–∞, 1)

Also, x¹⁰⁰¹ is defined for all x in R.

Hence, the domain of the given function 

= R ∩ (– ∞, 0) ∩ R

= (–∞, 1)