Question

Find the domain of f(x)= 10x+1 / 8x + 3 and put it in interval notation?

Answer 1

(- ∞, -
`(3)/(8)`) ∪ (-
`(3)/(8)`, ∞ )

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

solve : 8x + 3 = 0 ⇒ x = -
`(3)/(8)`

Answer 2

`f(x) = (10x + 1)/(8x + 3)`

8x + 3 ≠ 0

8x ≠ -3

`(8x)/(8) \\eq (-3)/(8)`

x ≠
`(-3)/(8)`

Interval Notation: (∞,
`(-3)/(8)`) U (
`(-3)/(8)`, ∞)