Q5: Car 1 brakes to a stop on a dry road. Car 2 does the same thing, at the same speed, on a road where it has been raining.
2 answers:
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Answer:
The function h (x) = StartFraction 11 Over x minus 4 EndFraction
has the domain of h (x) = ( - ∞, 4) U (4, ∞ ) which is same as the
domain of (m ∘ n)(x) = ( - ∞, 4) U (4, ∞ ).
Step-by-step explanation:
m (x) = StartFraction x + 5 Over x minus 1 and n(x) = x – 3
As m (x) could be written as:
n(x) = x – 3
(m ∘ n)(x) = m(n(x)) = m(x – 3)
=
=
In order to find the domain of (m ∘ n)(x) = , we need to
make sure that denominator can not be zero,
So,
x - 4 = 0
x = 4
So, our domain can be anything except for 4.
Hence, Domain = D = ( - ∞, 4) U (4, ∞ )
Now, compare the domain of (m ∘ n)(x) i.e D = ( - ∞, 4) U (4, ∞ ) with all the options:
Option A: h (x) = x + 5 / 11
Option A has the Domain of h (x) = Set of all real numbers
So, Option A is false.
Option B: h (x) = 11 / x - 1
x - 1 = 0
x = 1
Option B has the domain of h (x) = ( - ∞, 1) U (1, ∞ )
So, Option B is false.
Option C: h (x) = 11 / x - 4
x - 4 = 0
x = 4
Domain C has the domain of h (x) = ( - ∞, 4) U (4, ∞ )
So, Option C is true.
Option D: h (x) = 11 / x - 3
x - 3 = 0
x = 3
Option D has the domain of h (x) = ( - ∞, 3) U (3, ∞ )
So, option D is also false.
Hence, only option C is true as the option C i.e. h (x) = StartFraction 11 Over x minus 4 EndFraction has the domain of h (x) = ( - ∞, 4) U (4, ∞ ) which is same as the domain of (m ∘ n)(x) = ( - ∞, 4) U (4, ∞ ).
keywords: Domain, composite function
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Answer:
The answer is D.
Step-by-step explanation:
We have to apply Discriminant Law. When a quadratic equation, ax² + bx + c = 0 has equal roots so the discriminant will be 0. Then, you have to substitute the values into the formula :
YOU CANNOT ADD OR SUBTRACT FRACTIONS WITH DIFFERENT DENOMINATORS!! You need to find the LCD (Lowest Common Denominator) for 6 and 2 with is 6!!
(CORRECTED WORK SHOWN BELOW)
(CORRECTED WORK SHOWN BELOW)