Question

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

Answer 1

$f(x) = \frac{10x + 1}{8x + 3}$

8x + 3 ≠ 0

8x      ≠ -3

$\frac{8x}{8} \neq \frac{-3}{8}$

   x ≠ $\frac{-3}{8}$

Interval Notation: (∞,  $\frac{-3}{8}$) U ( $\frac{-3}{8}$, ∞)

Answer 2

(- ∞, -$\frac{3}{8}$) ∪ (- $\frac{3}{8}$, ∞ )

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 = - $\frac{3}{8}$