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Popular >

range of f(x)=x^2-4x+5

Solution

range

f (x) = x^{2} - 4 x + 5

Solution

f (x) \geq 1

+1

Interval Notation

[1, \infty)

Solution steps

Vertex of

x^{2} - 4 x + 5 :

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

domain of f(x)= 1/(2+x)domain

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

inverse of 8-3e^x inverse

8 - 3 e^{x}

monotone (2-x)e^{-x}-1 monotone intervals

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

intercepts of (x^2-4x+4)/(x^3-5x^2)intercepts

\frac{x ^{2} - 4 x + 4}{x ^{3} - 5 x ^{2}}

slope ofintercept (3-4)m=-4 slope intercept

(3 - 4) m = - 4

Frequently Asked Questions (FAQ)

What is the range of f(x)=x^2-4x+5 ?
The range of f(x)=x^2-4x+5 is f(x)>= 1