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Popular >

range of (x^2+1)/2

Solution

range

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

Solution

f (x) \geq \frac{1}{2}

+1

Interval Notation

[\frac{1}{2}, \infty)

Solution steps

Vertex of

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

Minimum

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

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}{2},

Vertex

(x_{v}, y_{v}) = (0, \frac{1}{2})

f (x) \geq \frac{1}{2}

Popular Examples

domain of (x^2+7x)/(5x^2-1)domain

\frac{x ^{2} + 7 x}{5 x ^{2} - 1}

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

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

asymptotes of f(x)= 5/((x-2)^2)asymptotes

f (x) = \frac{5}{( x - 2 ) ^{2}}

inverse of f(x)=6-2x^2 inverse

f (x) = 6 - 2 x^{2}

range of f(x)=5^{x-2}range

f (x) = 5^{x - 2}

Frequently Asked Questions (FAQ)

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