Question

Determine the domain of the function showing the steps.

Algebra

Answer 1

[-2, 7) ∪ (7, ∞)

Explanation:

Given function is,

f(x) =
`(0.1√(4x+8) )/(x-7)`

This function is defined only when

`4x + 8 \geq 0` [Since square root of a number is not defined]

4x ≥ -8

x ≥ -2

And denominator is greater than of equal to zero.

(If the denominator of a fraction is zero, fraction is not defined)

x - 7 ≥ 0

x ≥ 0

Therefore, domain of the given function will be,

[-2, 7) ∪ (7, ∞)