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Popular >

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

Solution

range

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

Solution

f (x) \geq - 1

+1

Interval Notation

[- 1, \infty)

Solution steps

Vertex of

(x - 2)^{2} - 1 :

Minimum

(2, - 1)

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}) = (2, - 1)

f (x) \geq - 1

Popular Examples

inverse of f(x)=\sqrt[3]{x-9}inverse

intercepts of (x+3)/(sqrt(x^2-1))intercepts

\frac{x + 3}{x ^{2} - 1}

y = 4 + 2 x - x^{2}

range of sqrt(x+9)range

x + 9

simplify (6.5)(4.6)simplify

(6.5) (4.6)

Frequently Asked Questions (FAQ)

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