Question

find domain of
f(x)= (10 ^x + 10^-x)/(10^x - 10^-x)​

Answer 1

Answer:

10x + 10y = 10

⇒ 10y = 10 – 10x

⇒ 10y = 10 (1 – 10x – 1)

⇒ log10 10y = log10 10 + log10 (1 – 10x – 1)

⇒ y = 1 + log10 (1 – 10x – 1)

Now, for y to be defined log10 (1 – 10x – 1) must be defined.

i.e., 1 – 10x – 1 > 0

⇒ 1 > 10x – 1

⇒ 10 > 10x

i.e. 10x < 101

⇒ x < 1

∴ Domain: (– ∞