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

The range of (x^2-2x+1)/(x^3-3x^2) is -infinity <f(x)<infinity

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range of (x^2-2x+1)/(x^3-3x^2)

range

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

- \infty < f (x) < \infty

Solution steps

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

Domain of

\frac{x ^{2} - 2 x + 1}{x ^{3} - 3 x ^{2}} : x < 0 or 0 < x < 3 or x > 3

Extreme Points of

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

Maximum

(1, 0)

Find the range for the interval

- \infty < x < 0 : - \infty < f (x) < 0

Find the range for the interval

0 < x < 3 : - \infty < f (x) \leq 0

Find the range for the interval

3 < x < \infty : 0 < f (x) < \infty

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

f (x) < 0 or f (x) \leq 0 or f (x) > 0

- \infty < f (x) < \infty

f (x) = 6 x + 4

\frac{4 x ^{2} + 6 x - 4}{2 x ^{2} + 13 x + 15}

f (x) = 2 + x - 3

f (x) = - (\frac{1}{5})^{x}

- tan (x)

What is the range of (x^2-2x+1)/(x^3-3x^2) ?
The range of (x^2-2x+1)/(x^3-3x^2) is -infinity <f(x)<infinity