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Popular >

f(x)=((4x-3)^3)/((2x-3)^4)

Solution

f (x) = \frac{( 4 x - 3 ) ^{3}}{( 2 x - 3 ) ^{4}}

Solution

Domain : x < \frac{3}{2} or x > \frac{3}{2}

Range : f (x) \geq - \frac{9}{16}

X Intercepts : (\frac{3}{4}, 0), Y Intercepts : (0, - \frac{1}{3})

Asymptotes : Vertical x = \frac{3}{2}, Horizontal y = 0

Extreme Points : Minimum (- \frac{3}{2}, - \frac{9}{16}), Saddle (\frac{3}{4}, 0)

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Interval Notation

Domain : (- \infty, \frac{3}{2}) \cup (\frac{3}{2}, \infty)

Range : [- \frac{9}{16}, \infty)

Solution steps

Domain of

\frac{( 4 x - 3 ) ^{3}}{( 2 x - 3 ) ^{4}} : x < \frac{3}{2} or x > \frac{3}{2}

Range of

\frac{( 4 x - 3 ) ^{3}}{( 2 x - 3 ) ^{4}} : f (x) \geq - \frac{9}{16}

Axis interception points of

\frac{( 4 x - 3 ) ^{3}}{( 2 x - 3 ) ^{4}} :

X Intercepts

: (\frac{3}{4}, 0),

Y Intercepts

: (0, - \frac{1}{3})

Asymptotes of

\frac{( 4 x - 3 ) ^{3}}{( 2 x - 3 ) ^{4}} :

Vertical

: x = \frac{3}{2},

Horizontal

: y = 0

Extreme Points of

\frac{( 4 x - 3 ) ^{3}}{( 2 x - 3 ) ^{4}} :

Minimum

(- \frac{3}{2}, - \frac{9}{16}),

Saddle

(\frac{3}{4}, 0)

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Frequently Asked Questions (FAQ)

What is the f(x)=((4x-3)^3)/((2x-3)^4) ?
The f(x)=((4x-3)^3)/((2x-3)^4) is