Question

8.7 use radicals in functions (homework)
score: 7/10 answered: 8/10
question 9
find the domain of $f(x)=sqrt{\frac{2}{4x - 3}}$.
the domain is $xin$ (enter your answer in interval notation)

Explanation:

Step1: Set the expression inside square - root non - negative

$\frac{2}{4x - 3}\geq0$
Since the numerator $2>0$, we need to consider the sign of the denominator.

Step2: Analyze the denominator

For $\frac{2}{4x - 3}\geq0$, we need $4x-3>0$ (because a positive numerator divided by a positive denominator is non - negative).
Solve the inequality $4x - 3>0$.
Add 3 to both sides: $4x>3$.
Divide both sides by 4: $x>\frac{3}{4}$.

Answer:

$(\frac{3}{4},\infty)$