Answer:
19) The domain is (12 , ∞) ⇒ answer C
17) The radical notation is [tex]\sqrt[7]{18y^{2} }[/tex]
10) The definition of number i is √(-1) ⇒ answer C
Step-by-step explanation:
19)
* Lets explain the meaning of the domain of the function
- The domain of any function is the values of x which makes the
function defined
- Examples:
# In the fraction the denominator con not be zero, then if the function
is a rational fraction then the domain is all the values of x except
the values whose make the denominator = 0
# In the even roots we can not put negative numbers under the radical
because there is no even roots for the negative number belonges to
the real numbers, then the domain is all the values of x except the
values whose make the quantity under the radical negative
* Now lets solve the question
∵ f(x) = 3 √(x - 12)
- To find the domain let (x - 12) greater than zero because there is
no square root for negative value
∵ x - 12 > 0 ⇒ add 12 to both sides
∴ x ≥ 12
∴ The domain is all values of x greater than 12
* The domain is (12 , ∞)
17)
* Lets talk about the radical notation
- The radical notation for the fraction power is:
the denominator of the power will be the radical and the numerator
of the power will be the power of the base
- Ex: [tex]x^{\frac{a}{b}}=\sqrt[b]{x^{a}}[/tex]
* Lets solve the problem
∵ (18 y²)^(1/7)
- The power 1/7 will be the radical over (18 y²)
∴ [tex](18y^{2})^{\frac{1}{7}}=\sqrt[7]{18y^{2}}[/tex]
* The radical notation is [tex]\sqrt[7]{18y^{2} }[/tex]
10)
* Lets talk about the imaginary number
- Because there is no even root for negative number, the imaginary
numbers founded to solve this problem
- It is a complex number that can be written as a real number multiplied
by the imaginary unit i, which is defined by i = √(-1) or i² = -1
- Ex: √(-5) = √[-1 × 5] = i√5
* The definition of number i is √(-1)
