ANSWER
EXPLANATION
We want to evaluate
Use indices to rewrite the expression as:
We know that
So we rewrite the expression to obtain;
This gives us;
This simplifies to
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.
9514 1404 393
Answer:
(X, Y, Z) = (-2, 3, 3)
Step-by-step explanation:
We can subtract the second equation from the first to get ...
Y -Z = 0
We can add the third equation to the first to get ...
Z = 3
Then ...
Y -3 = 0 ⇒ Y = 3
and ...
X -3 -2(3) = -11
X = -2 . . . . . . . . . add 9
The solution is ...
(X, Y, Z) = (-2, 3, 3)
Answer:
-15
Step-by-step explanation:
Well you cleary just divide the numbers But if you dont belive it use a caculator for this
Answer:
y = 1
Step-by-step explanation:
x + y = 16
x - y = 14 add the equations
--------------
2x = 30
x = 15
x + y = 16
15 + y = 16
y = 1
the numbers are 15 and 1
