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Popular >

range of f(x)=(1+x^2)/4

Solution

range

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

Solution

f (x) \geq \frac{1}{4}

+1

Interval Notation

[\frac{1}{4}, \infty)

Solution steps

Vertex of

\frac{1 + x ^{2}}{4} :

Minimum

(0, \frac{1}{4})

For a parabola

a x^{2} + b x + c

with Vertex

(x_{v}, y_{v})

If

a < 0

the range is

f (x) \leq y_{v}

If

a > 0

the range is

f (x) \geq y_{v}

a = \frac{1}{4},

Vertex

(x_{v}, y_{v}) = (0, \frac{1}{4})

f (x) \geq \frac{1}{4}

Popular Examples

domain of f(x)=(sqrt(4+x))/(1-x)domain

f (x) = \frac{4 + x}{1 - x}

inflection (x-3)/(x+5)inflection points

\frac{x - 3}{x + 5}

line m=-8/3 ,(4,1)line

m = - \frac{8}{3}, (4, 1)

inverse of f(x)= 2/3 (x-2)^3+6 inverse

f (x) = \frac{2}{3} (x - 2)^{3} + 6

extreme f(x)=6sqrt(x)-6x extreme points

f (x) = 6 x - 6 x

Frequently Asked Questions (FAQ)

What is the range of f(x)=(1+x^2)/4 ?
The range of f(x)=(1+x^2)/4 is f(x)>= 1/4