Answer:
![f^{-1}(x)=\sqrt[3]{x}-1](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Csqrt%5B3%5D%7Bx%7D-1)
Step-by-step explanation:
![f(x)=(x+1)^3\\\\y=(x+1)^3\\\\x=(y+1)^3\\\\\sqrt[3]{x}=y+1\\\\y=\sqrt[3]{x}-1\\ \\f^{-1}(x)=\sqrt[3]{x}-1](https://tex.z-dn.net/?f=f%28x%29%3D%28x%2B1%29%5E3%5C%5C%5C%5Cy%3D%28x%2B1%29%5E3%5C%5C%5C%5Cx%3D%28y%2B1%29%5E3%5C%5C%5C%5C%5Csqrt%5B3%5D%7Bx%7D%3Dy%2B1%5C%5C%5C%5Cy%3D%5Csqrt%5B3%5D%7Bx%7D-1%5C%5C%20%5C%5Cf%5E%7B-1%7D%28x%29%3D%5Csqrt%5B3%5D%7Bx%7D-1)
Graphing both inverses, they will be symmetrical about the line 
.
PART A:
Scientific notation is given by A×10ⁿ where A is any number in a unit and 'n' is an integer.
0.000025 = 2.5×10⁻⁵
PART B:
Diameter of grain of sand ÷ Diameter of human body average cell
(2×10⁻⁴) ÷ (1×10⁻⁵)
(2÷1) × (10⁻⁴÷10⁻⁵)
2 × (10⁻⁴ ⁻ ⁻⁵) = 2 × 10⁽⁻⁴⁺⁵⁾ = 2 × 10¹ = 20 times bigger
PART C:
The diameter of human body's average cell in nanometer
1 × 10⁻⁵ metre = 1 × 10⁻⁵ × 10⁹ = 1 × 10⁽⁻⁵⁺⁹⁾ = 1 × 10⁴ nanometer
PART D:
Smallest bacteria = 300 nanometer
300 nm = 300 ÷ 10⁹ = (3 × 10²) ÷ 10⁹ = 3 × (10²⁻⁹) = 3 × 10⁻⁷ meter
PART E:
Laws of exponents that are applied in scientific notation is
xᵇ × xᵃ = x⁽ᵇ⁺ᵃ⁾
xᵇ ÷ xᵃ = x⁽ᵇ⁻ᵃ⁾
Answer:
A straight line.
Step-by-step explanation:
An arithmetic sequence has a common difference so the slope of the graph will be constant, giving a straight line.
Answer:
The series
1 -0.5-2-3.5 -5-6.5-8-9.5-11-12.5-14-15.5 upto 12 terms
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
Given series 1 -0.5 -2 +.........
we know that the sum of the sequence is called a series
The sequence is 1, -0.5, -2, -3.5,.....is in AP
a = 1 and the difference between the two terms is equal 'd' = -1.5
<u><em>Step(ii):-</em></u>
<u><em>adding 1.5 value of each term</em></u>
The series
1 -0.5-2-3.5 -5-6.5-8-9.5-11-12.5-14-15.5 upto 12 terms
<u><em></em></u>
