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Popular Functions >

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

Solution

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

Solution

Domain : - \infty < x < \infty

Range : - \frac{1}{8} \leq f (x) < 0 or 0 < f (x) \leq 1

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

Asymptotes : Horizontal y = 0

Extreme Points : Minimum (- 3, - \frac{1}{8}), Maximum (0, 1), Minimum (3, - \frac{1}{8})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{1}{8}, 0) \cup (0, 1]

Solution steps

Domain of

\frac{1 - x ^{2}}{( 1 + x ^{2} ) ^{2}} : - \infty < x < \infty

Range of

\frac{1 - x ^{2}}{( 1 + x ^{2} ) ^{2}} : - \frac{1}{8} \leq f (x) < 0 or 0 < f (x) \leq 1

Axis interception points of

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

X Intercepts

: (1, 0), (- 1, 0),

Y Intercepts

: (0, 1)

Asymptotes of

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

Horizontal

: y = 0

Extreme Points of

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

Minimum

(- 3, - \frac{1}{8}),

Maximum

(0, 1),

Minimum

(3, - \frac{1}{8})

Graph

Popular Examples

f(x)=-log_{3}(x)+2

y=-16x^2+168x+92

Frequently Asked Questions (FAQ)

What is the f(x)=(1-x^2)/((1+x^2)^2) ?
The f(x)=(1-x^2)/((1+x^2)^2) is