Answer:
#3 a. g(-1) = 2, g(0) = 3, and g(1) = 2
b. No restrictions for all real numbers
b. Yes, <em>x ≠ 2</em>
Step-by-step explanation:
#3 The function is given as g(x) = -x² + 3
a. From the given function, by plugging in the value of 'x' in the bracket, we have;
g(-1) = -(-1)² + 3 = -1 + 3 = 2
g(-1) = 2
g(0) = -0² + 3 = 3
g(0) = 3
g(1) = -1² + 3 = -1 + 3 = 2
g(1) = 2
g(-1) = 2, g(0) = 3, and g(1) = 2
b. The given function g(x) = -x² + 3 for finding the value of <em>g</em> can take any value of <em>x</em> which is a real number
Therefore, therefore, there are no restrictions
#4 a. The given function is given as follows;
By substitution, we get;
b. From the values of the function, we have that h(x) is not defined at x = 2
Therefore, there is a restriction for <em>x</em> in the function, which is <em>x ≠ 2</em>
Answer:
Step-by-step explanation:
Cancel out 6 in both numerator and denominator.
Rationalize the denominator of by multiplying the numerator and denominator by 
.
The square of is 2
Factor 14=2 × 7. Rewrite the square root of the product 
as the product of square roots 
.
Multiply and to get 2.
Cancel out 2 and 2.
Hope it helps and have a great day! =D
C. 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60
1,000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
Now we find the common numbers. One doesn’t count as when multiplied later on, it will not change anything.
60: 2, 4, 5, 10, 20
1,000: 2, 4, 5, 10, 20
The highest common factor is 20 because it’s, well, the highest number.
D. Do the same thing for D.
24: 1, 2, 3, 4, 6, 8, 12, 24
880: 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440, 880
20 and 880: 2, 4, 8
8 is the Highest Common Factor.
E. Do the same thing with E.
90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
1,000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
90 and 1000: 2, 5, 10
10 is the Highest Common Factor.
