What is the range of (2x)/(sqrt(3x-1)) ?

The range of (2x)/(sqrt(3x-1)) is f(x)>= 4/3

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range of (2x)/(sqrt(3x-1))

range

\frac{2 x}{3 x - 1}

f (x) \geq \frac{4}{3}

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

\frac{2 x}{3 x - 1} : x > \frac{1}{3}

Extreme Points of

\frac{2 x}{3 x - 1} :

Minimum

(\frac{2}{3}, \frac{4}{3})

Find the range for the interval

\frac{1}{3} < x < \infty : \frac{4}{3} \leq f (x) < \infty

Combine the ranges of all domain intervals to obtain the function range

f (x) \geq \frac{4}{3}

- x^{4} + 2 x^{3} + 4 x^{2}

y = \frac{3}{4} x + 3

y = 2 - \frac{1}{2} x

f (x) = (8 x - 1) + (- 7 x^{2})

f (x) = \frac{4 x ^{2} - 7 x - 2}{x ^{2} + 1}

What is the range of (2x)/(sqrt(3x-1)) ?
The range of (2x)/(sqrt(3x-1)) is f(x)>= 4/3