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Popular >

f(x)=((x-1))/((x^2+x-1))

Solution

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

Solution

Domain : x < \frac{- 1 - 5}{2} or \frac{- 1 - 5}{2} < x < \frac{- 1 + 5}{2} or x > \frac{- 1 + 5}{2}

Range : f (x) \leq \frac{1}{5} or f (x) \geq 1

X Intercepts : (1, 0), Y Intercepts : (0, 1)

Asymptotes : Vertical x = \frac{- 1 - 5}{2}, x = \frac{- 1 + 5}{2}, Horizontal y = 0

Extreme Points : Minimum (0, 1), Maximum (2, \frac{1}{5})

+1

Interval Notation

Domain : (- \infty, \frac{- 1 - 5}{2}) \cup (\frac{- 1 - 5}{2}, \frac{- 1 + 5}{2}) \cup (\frac{- 1 + 5}{2}, \infty)

Range : (- \infty, \frac{1}{5}] \cup [1, \infty)

Solution steps

Domain of

\frac{x - 1}{x ^{2} + x - 1} : x < \frac{- 1 - 5}{2} or \frac{- 1 - 5}{2} < x < \frac{- 1 + 5}{2} or x > \frac{- 1 + 5}{2}

Range of

\frac{x - 1}{x ^{2} + x - 1} : f (x) \leq \frac{1}{5} or f (x) \geq 1

Axis interception points of

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

X Intercepts

: (1, 0),

Y Intercepts

: (0, 1)

Asymptotes of

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

Vertical

: x = \frac{- 1 - 5}{2}, x = \frac{- 1 + 5}{2},

Horizontal

: y = 0

Extreme Points of

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

Minimum

(0, 1),

Maximum

(2, \frac{1}{5})

Popular Examples

f(x)=8x^6+19x^3-3

f (x) = 8 x^{6} + 19 x^{3} - 3

f(x)=\sqrt[4]{(x^3+1)/(x^3-1)}

f(x)=-0.5x^2+40x-300

f (x) = - 0.5 x^{2} + 40 x - 300

y = 2 (x - 1)^{2} + 4

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

Frequently Asked Questions (FAQ)

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