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Popular >

range of 2(x-1)^2+1

Solution

range

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

Solution

f (x) \geq 1

+1

Interval Notation

[1, \infty)

Solution steps

Vertex of

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

Minimum

(1, 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 = 2,

Vertex

(x_{v}, y_{v}) = (1, 1)

f (x) \geq 1

Popular Examples

inverse of f(x)=log_{10}(x-3)inverse

f (x) = lo g_{10} (x - 3)

W(x)=9x^3+x^2-729x+81

W (x) = 9 x^{3} + x^{2} - 729 x + 81

domain of (7/x)-(9/(x+9))domain

(\frac{7}{x}) - (\frac{9}{x + 9})

inverse of f(x)=(5x)/(7x-1)inverse

f (x) = \frac{5 x}{7 x - 1}

domain of f(x)=(5x)/(ln(x^2-4))domain

f (x) = \frac{5 x}{ln ( x ^{2} - 4 )}

Frequently Asked Questions (FAQ)

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