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Popular >

f(z)=z^2+4z+1

Solution

f (z) = z^{2} + 4 z + 1

Solution

Domain : - \infty < z < \infty

Range : f (z) \geq - 3

X Intercepts : (- 2 + 3, 0), (- 2 - 3, 0), Y Intercepts : (0, 1)

Vertex : Minimum (- 2, - 3)

Inverse : - 2 + z + 3, - z + 3 - 2

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 3, \infty)

Solution steps

Domain of

z^{2} + 4 z + 1 : - \infty < z < \infty

Range of

z^{2} + 4 z + 1 : f (z) \geq - 3

Axis interception points of

z^{2} + 4 z + 1 :

X Intercepts

: (- 2 + 3, 0), (- 2 - 3, 0),

Y Intercepts

: (0, 1)

Vertex of

z^{2} + 4 z + 1 :

Minimum

(- 2, - 3)

Inverse of

z^{2} + 4 z + 1 : - 2 + z + 3, - z + 3 - 2

Popular Examples

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f (x) = \frac{x + 4 - x}{2}

f(x)= 1/(x^2)+sqrt(x^3)-4e^x+x-63

f (x) = \frac{1}{x ^{2}} + x^{3} - 4 e^{x} + x - 63

f(x)=5x^2+10x-2

f (x) = 5 x^{2} + 10 x - 2

y=(2x)/((x-3)^2)

y = \frac{2 x}{( x - 3 ) ^{2}}

f (x) = 2 - 1

Frequently Asked Questions (FAQ)

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