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:
A. 35
Step-by-step explanation:
The total amount of movies that the critic rates that we are given is 20. Now they want to figure us to figure it out with 100 movies. 20 times 5 is one hundred. We are supposed to look at the 3 star reviews, which is 7 movies. 7 times 5 is 35. Hope this helps!
Answer:
D pi/4, 3pi/4
Step-by-step explanation:
Differentiate the function then equal it to zero and solve for the interval (see attached workings)
Hello,
Degre 5==> even number of imaginary roots and odd number of reals.
Real roots must be a divisor of 7.
Using Excel, we find
<span>
<span><span>
x
P(x)
</span><span>-7
0
</span>
<span>
-6
1369
</span>
<span>
-5
1352
</span>
<span>
-4
867
</span>
<span>
-3
400
</span>
<span>
-2
125
</span>
<span>
-1
24
</span><span>0
7
</span><span>1
32
</span><span>2
225
</span><span>3
1000
</span><span>4
3179
</span><span>5
8112
</span><span>6
17797
</span><span>7
35000
So: one real root: 7 and 4 imaginary roots.
Answer B
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