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Popular Functions >

range of f(x)=(2x-1)^2

Solution

range

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

Solution

f (x) \geq 0

+1

Interval Notation

[0, \infty)

Solution steps

Vertex of

(2 x - 1)^{2} :

Minimum

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

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 = 4,

Vertex

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

f (x) \geq 0

Graph

Popular Examples

inverse of y=2x+2

domain of sqrt(10x+2)

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inverse of f(x)=x^2-16x+90

midpoint (2,-6),(4,8)

Frequently Asked Questions (FAQ)

What is the range of f(x)=(2x-1)^2 ?
The range of f(x)=(2x-1)^2 is f(x)>= 0