Answer:
(
h
∘
f
∘
g
)
(
x
)
is known as a composite function. Here's how composite functions work:
let's say that
x
=
1
. Your function
g
(
x
)
=
1
3
(
x
)
now produces a
y
output of
1
3
, since
g
(
1
)
=
1
3
(
1
)
. Within a composite function, the y-value of one function becomes the x-value of the next, like so:
g
(
1
)
=
1
3
⇒
f
(
1
3
)
=
17
3
⇒
h
(
17
3
)
=
17
Therefore,
(
h
∘
f
∘
g
)
(
1
)
=
17
Based on this, to find the function for
(
h
∘
f
∘
g
)
(
x
)
(combined from right to left, by the way), simply replace
x
in
f
(
x
)
with the function
g
(
x
)
, and replace
x
in
h
(
x
)
with the function of
(
f
∘
g
)
(
x
)
, to get
(
h
∘
f
∘
g
)
(
x
)
.
This, simplified, is equal to
2
x
+
15
, and therefore
(
h
∘
f
∘
g
)
(
1
)
=
2
(
1
)
+
15
=
17
Hope that helps!
Answer:x=−24/11
Step-by-step explanation:
Simplifies to:
x−86x=79
Let's solve your equation step-by-step.
x−86x=79
Step 1: Cross-multiply.
x−86x=79
(x−8)*(9)=7*6x
9x−72=42x
Step 2: Subtract 42x from both sides.
9x−72−42x=42x−42x
−33x−72=0
Step 3: Add 72 to both sides.
−33x−72+72=0+72
−33x=72
Step 4: Divide both sides by -33.
−33x−33=72−33
x=−2411
Answer:
Step-by-step explanation:
First, simplify each term:
Then given expression is equivalent to
![\cos ^3\alpha+(-\sin \alpha)^3-(-\sin \alpha)+(-\cos \alpha)\\ \\=\cos ^3\alpha-\sin^3 \alpha+\sin \alpha-\cos \alpha\\ \\=(\cos\alpha-\sin\alpha)(\cos^2\alpha+\cos\alpha\sin\alpha+\sin^2\alpha)-(\cos\alpha-\sin\alpha)\\ \\=(\cos\alpha-\sin\alpha)(1+\cos\alpha\sin\alpha-1)\ \ [\cos^2\alpha+\sin^2\alpha=1]\\ \\=\cos\alpha\sin\alpha(\cos\alpha-\sin\alpha)](https://tex.z-dn.net/?f=%5Ccos%20%5E3%5Calpha%2B%28-%5Csin%20%5Calpha%29%5E3-%28-%5Csin%20%5Calpha%29%2B%28-%5Ccos%20%5Calpha%29%5C%5C%20%5C%5C%3D%5Ccos%20%5E3%5Calpha-%5Csin%5E3%20%5Calpha%2B%5Csin%20%5Calpha-%5Ccos%20%5Calpha%5C%5C%20%5C%5C%3D%28%5Ccos%5Calpha-%5Csin%5Calpha%29%28%5Ccos%5E2%5Calpha%2B%5Ccos%5Calpha%5Csin%5Calpha%2B%5Csin%5E2%5Calpha%29-%28%5Ccos%5Calpha-%5Csin%5Calpha%29%5C%5C%20%5C%5C%3D%28%5Ccos%5Calpha-%5Csin%5Calpha%29%281%2B%5Ccos%5Calpha%5Csin%5Calpha-1%29%5C%20%5C%20%5B%5Ccos%5E2%5Calpha%2B%5Csin%5E2%5Calpha%3D1%5D%5C%5C%20%5C%5C%3D%5Ccos%5Calpha%5Csin%5Calpha%28%5Ccos%5Calpha-%5Csin%5Calpha%29)
Answer:
option 4
Step-by-step explanation:
Using the rule of radicals
× 
= 
Given
(2 - 5
) 3
← distribute parenthesis by 3
= 6 - 15
= 6 - 15
= 6 - 15(
× 
)
= 6 - 15(2 )
= 6 - 30
Answer:
Where h,k represent the vertex and we got:
(5,6)
Step-by-step explanation:
We have this original function given :
And we want to find the vertex for this new function 
and we have:
And solving the square we got:
And adding similar terms we got:
Now we can complete the square like this:
The general equation is given by:
Where h,k represent the vertex and we got:
(5,6)
