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Popular Functions >

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}

Graph

Popular Examples

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

inverse of f(x)=-2x-7

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