TS Inter 1st Year Maths 1A Solutions Chapter 1 Functions Ex 1(c)

TS Inter 1st Year Maths 1A Functions Solutions Exercise 1(c)
I.
Question 1.
Find the domains of the following real valued functions. (May 2014, Mar. 14)
(i) f(x) = 1/(x²−1)(x+3)
Answer:
Domain of f is the value of all real x for which (x² – 1) (x + 3) ≠ 0
⇔ (x + 1) (x – 1) (x + 3) ≠ 0
⇔ x ≠ – 1, 1, -3
∴ Domain of f is, R – {-1, 1, – 3}
(ii) f(x) = 2x²−5x+7/(x−1)(x−2)(x−3)
Answer:
Here (x – 1) (x – 2) (x – 3) + 0
⇔ x ≠ 1, x ≠ 2, x ≠ 3.
Domain of f is, R – {1, 2, 3}
(iii) f(x) = 1/log(2−x)
Answer:
f(x) = 1/log(2−x) ∈ R
⇔ log (2 – x) ≠ 0 and 2 – x > 0
⇔ 2 – x ≠ 1 and 2 > x
⇔ x ≠ 1 and x < 2
⇔ x ∈ (-∞, 1) U (1, 2)
(or) x ∈ (-∞, 2) – {1}
Domain of f = x ∈ {∞, 2} – {1}