What is the f(a)=a^{12}-6a^8+5a^4+2a^6-6a^2+1 ?

The f(a)=a^{12}-6a^8+5a^4+2a^6-6a^2+1 is

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f(a)=a^{12}-6a^8+5a^4+2a^6-6a^2+1

f (a) = a^{12} - 6 a^{8} + 5 a^{4} + 2 a^{6} - 6 a^{2} + 1

Domain : - \infty < a < \infty

Range : f (x) \geq - \frac{1.1897 E 15}{1.25 E 14} + \frac{8.76468 E 1 5 ^{6}}{5.0 E 1 5 ^{6}} - \frac{8.76468 E 1 5 ^{4} \cdot 6}{5.0 E 1 5 ^{4}} + \frac{8.76468 E 1 5 ^{2} \cdot 5}{5.0 E 1 5 ^{2}} + \frac{8.76468 E 1 5 ^{3} \cdot 2}{5.0 E 1 5 ^{3}}

X Intercepts : (0.20163 \dots, 0), (- 0.20163 \dots, 0), (2.12841 \dots, 0), (- 2.12841 \dots, 0), Y Intercepts : (0, 1)

Asymptotes : Horizontal y = a^{12} - 6 a^{8} + 5 a^{4} + 2 a^{6} - 6 a^{2} + 1

Extreme Points : Minimum (- \frac{8.76468 E 15}{5.0 E 15}, - \frac{1.1897 E 15}{1.25 E 14} + \frac{8.76468 E 1 5 ^{6}}{5.0 E 1 5 ^{6}} - \frac{8.76468 E 1 5 ^{4} \cdot 6}{5.0 E 1 5 ^{4}} + \frac{8.76468 E 1 5 ^{2} \cdot 5}{5.0 E 1 5 ^{2}} + \frac{8.76468 E 1 5 ^{3} \cdot 2}{5.0 E 1 5 ^{3}}), Maximum (0, 1), Minimum (\frac{8.76468 E 15}{5.0 E 15}, - \frac{1.1897 E 15}{1.25 E 14} + \frac{8.76468 E 1 5 ^{6}}{5.0 E 1 5 ^{6}} - \frac{8.76468 E 1 5 ^{4} \cdot 6}{5.0 E 1 5 ^{4}} + \frac{8.76468 E 1 5 ^{2} \cdot 5}{5.0 E 1 5 ^{2}} + \frac{8.76468 E 1 5 ^{3} \cdot 2}{5.0 E 1 5 ^{3}})

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{1.1897 E 15}{1.25 E 14} + \frac{8.76468 E 1 5 ^{6}}{5.0 E 1 5 ^{6}} - \frac{8.76468 E 1 5 ^{4} 6}{5.0 E 1 5 ^{4}} + \frac{8.76468 E 1 5 ^{2} 5}{5.0 E 1 5 ^{2}} + \frac{8.76468 E 1 5 ^{3} 2}{5.0 E 1 5 ^{3}}, \infty)

Solution steps

Domain of

a^{12} - 6 a^{8} + 5 a^{4} + 2 a^{6} - 6 a^{2} + 1 : - \infty < a < \infty

Range of

a^{12} - 6 a^{8} + 5 a^{4} + 2 a^{6} - 6 a^{2} + 1 : f (x) \geq - \frac{1.1897 E 15}{1.25 E 14} + \frac{8.76468 E 1 5 ^{6}}{5.0 E 1 5 ^{6}} - \frac{8.76468 E 1 5 ^{4} \cdot 6}{5.0 E 1 5 ^{4}} + \frac{8.76468 E 1 5 ^{2} \cdot 5}{5.0 E 1 5 ^{2}} + \frac{8.76468 E 1 5 ^{3} \cdot 2}{5.0 E 1 5 ^{3}}

Axis interception points of

a^{12} - 6 a^{8} + 5 a^{4} + 2 a^{6} - 6 a^{2} + 1 :

X Intercepts

: (0.20163 \dots, 0), (- 0.20163 \dots, 0), (2.12841 \dots, 0), (- 2.12841 \dots, 0),

Y Intercepts

: (0, 1)

Asymptotes of

a^{12} - 6 a^{8} + 5 a^{4} + 2 a^{6} - 6 a^{2} + 1 :

Horizontal

: y = a^{12} - 6 a^{8} + 5 a^{4} + 2 a^{6} - 6 a^{2} + 1

Extreme Points of

a^{12} - 6 a^{8} + 5 a^{4} + 2 a^{6} - 6 a^{2} + 1 :

Minimum

(- \frac{8.76468 E 15}{5.0 E 15}, - \frac{1.1897 E 15}{1.25 E 14} + \frac{8.76468 E 1 5 ^{6}}{5.0 E 1 5 ^{6}} - \frac{8.76468 E 1 5 ^{4} \cdot 6}{5.0 E 1 5 ^{4}} + \frac{8.76468 E 1 5 ^{2} \cdot 5}{5.0 E 1 5 ^{2}} + \frac{8.76468 E 1 5 ^{3} \cdot 2}{5.0 E 1 5 ^{3}}),

Maximum

(0, 1),

Minimum

(\frac{8.76468 E 15}{5.0 E 15}, - \frac{1.1897 E 15}{1.25 E 14} + \frac{8.76468 E 1 5 ^{6}}{5.0 E 1 5 ^{6}} - \frac{8.76468 E 1 5 ^{4} \cdot 6}{5.0 E 1 5 ^{4}} + \frac{8.76468 E 1 5 ^{2} \cdot 5}{5.0 E 1 5 ^{2}} + \frac{8.76468 E 1 5 ^{3} \cdot 2}{5.0 E 1 5 ^{3}})

y = - x - 3 + 4

f (x) = - 0.4 x^{2} + 90 x - 2000

C (t) = 6 t^{2} + 500 t + 8000

f (x) = lo g_{2} (4 x - 1)

f (x) = 6 x^{3} - 5 x^{2} + 3 x - 2

What is the f(a)=a^{12}-6a^8+5a^4+2a^6-6a^2+1 ?
The f(a)=a^{12}-6a^8+5a^4+2a^6-6a^2+1 is