Rational. Irrational are numbers that cannot be written as fractions. 8 can be written as a fraction. 8/1
Answer:
A.) gf(x) = 3x^2 + 12x + 9
B.) g'(x) = 2
Step-by-step explanation:
A.) The two given functions are:
f(x) = (x + 2)^2 and g(x) = 3(x - 1)
Open the bracket of the two functions
f(x) = (x + 2)^2
f(x) = x^2 + 2x + 2x + 4
f(x) = x^2 + 4x + 4
and
g(x) = 3(x - 1)
g(x) = 3x - 3
To find gf(x), substitute f(x) for x in g(x)
gf(x) = 3( x^2 + 4x + 4 ) - 3
gf(x) = 3x^2 + 12x + 12 - 3
gf(x) = 3x^2 + 12x + 9
Where
a = 3, b = 12, c = 9
B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)
To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula
Y = 3x + 3
X = 3y + 3
Make y the subject of formula
3y = x - 3
Y = x/3 - 3/3
Y = x/3 - 1
Therefore, g'(x) = x/3 - 1
For g'(12), substitute 12 for x in g' (x)
g'(x) = 12/4 - 1
g'(x) = 3 - 1
g'(x) = 2.
Answer:
x = ±sqrt(5/2)
Step-by-step explanation:
6x^2−2=13
Add 2 to each side
6x^2−2+2=13+2
6x^2 = 15
Divide each side by 6
6/6x^2 = 15/6
x^2 = 5/2
Take the square root of each side
sqrt(x^2) = ±sqrt(5/2)
x = ±sqrt(5/2)
4(3x + 12) = -6(-8-2x)
12x + 48 = 48 +12x
12x + 18 = 12x + 48
0 = 0
answer is A. infinitely many solutions
