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:
<em>The translation corresponds to a translation of 13 units to the right</em>
Step-by-step explanation:
<u>Translation of a Graph</u>
If the graph of
y=f(x) is translated a units horizontally, then the equation of the translated graph is
y =f(x - a)
The value of a is considered positive for translations to the right.
The parent function is
y = x
and the given function is
y = x - 13
The translation corresponds to a translation of 13 units to the right
idk
Step-by-step explanation:
im to tired this sucks
Answer:
(2x + 3)(x - 2)
Step-by-step explanation:
use FOIL
First, Outside, Inside, Last
2x x x = 2x²
2x x -2 = -4x
3 x x = 3x
3 x -2 = -6
2x² - 4x + 3x - 6
Answer:
C and F
Step-by-step explanation:
Given
(3x - 5)² = 19 ( take the square root of both sides )
3x - 5 = ± 
← note plus or minus
Add 5 to both sides
3x = ± + 5 ( divide both sides by 3 )
x = ±
Separating the solutions
x = 
→ C
x = 
→ F
