What is the y=(xsqrt(2x+1))/(sqrt(4-5x)) ?

The y=(xsqrt(2x+1))/(sqrt(4-5x)) is

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y=(xsqrt(2x+1))/(sqrt(4-5x))

y = \frac{x 2 x + 1}{4 - 5 x}

Domain : - \frac{1}{2} \leq x < \frac{4}{5}

Range : f (x) \geq - \frac{( 1001 - 19 ) 39 - 1001}{20 10 13 + 1001}

X Intercepts : (0, 0), (- \frac{1}{2}, 0), Y Intercepts : (0, 0)

Asymptotes : Vertical x = \frac{4}{5}

Extreme Points : Maximum (- \frac{1}{2}, 0), Minimum (- \frac{- 19 + 1001}{40}, - \frac{( 1001 - 19 ) 39 - 1001}{20 10 13 + 1001})

Interval Notation

Domain : [- \frac{1}{2}, \frac{4}{5})

Range : [- \frac{( 1001 - 19 ) 39 - 1001}{20 10 13 + 1001}, \infty)

Solution steps

Domain of

\frac{x 2 x + 1}{4 - 5 x} : - \frac{1}{2} \leq x < \frac{4}{5}

Range of

\frac{x 2 x + 1}{4 - 5 x} : f (x) \geq - \frac{( 1001 - 19 ) 39 - 1001}{20 10 13 + 1001}

Axis interception points of

\frac{x 2 x + 1}{4 - 5 x} :

X Intercepts

: (0, 0), (- \frac{1}{2}, 0),

Y Intercepts

: (0, 0)

Asymptotes of

\frac{x 2 x + 1}{4 - 5 x} :

Vertical

: x = \frac{4}{5}

Extreme Points of

\frac{x 2 x + 1}{4 - 5 x} :

Maximum

(- \frac{1}{2}, 0),

Minimum

(- \frac{- 19 + 1001}{40}, - \frac{( 1001 - 19 ) 39 - 1001}{20 10 13 + 1001})

y = - 5 x^{3} - 5 x^{2} + 280 x

f (x) = 2 x^{2} + 7 x - 15

y = 2 sin (x) cos (x)