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Popular >

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

Solution

range

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

Solution

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

+1

Solution steps

Vertex of

x - x^{2} :

Maximum

(\frac{1}{2}, \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 = - 1,

Vertex

(x_{v}, y_{v}) = (\frac{1}{2}, \frac{1}{4})

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

Popular Examples

parity (tan(θ))/θ parity

\frac{tan ( θ )}{θ}

range of (12)/x range

\frac{12}{x}

inverse of f(x)=\sqrt[5]{x+3}+1 inverse

distance (3,10),(10,11)distance

(3, 10), (10, 11)

inverse of f(x)=((x-1))/x inverse

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

Frequently Asked Questions (FAQ)

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