If f(X)= 7x +5/3 - x =6x +5/3
y= 6x +5/3
6x= y-5/3
f^-1(y)=x=(y-5/3)/6
So we can write
f(f^-1(y))= f((y-5/3)/6) = 6 (y-5/3)/6 +5/3= y-5/3+5/3= y
The same result can be obtained for f^-1(f(x))=x
If the function is f(x)= 7x +5/(3-x) then it is not invertible since it is not injective (pictures)
The answer is: [B]: (13, -5) .
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Explanation: Using Substitution:
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y = 8 − x ;
7 = 2 − y ;
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Solve for "x" and "y" using using substitution;
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Take the second equation given:
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7 = 2 − y ;
And considering the first equation given: " y = 8 − x " ;
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Substitute the value: "8 − x" for (the value of "y" in the first equation given), in order to solve for "x" ;
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7 = 2 − y ;
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7 = 2 − 8 − x ;
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7 = -6 − x ;
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Add "6" to EACH side of the equation:
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7 + 6 = -6 − x + 6 ;
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to get: 13 = -x ;
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13 = -x ; ↔ -x = 13 ; ↔ -1 x = 13 ;
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Divide EACH side of the equation by "-1 " ; to isolate "x" on one side of the equation; and to solve for "x" ;
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-1 x / -1 = 13 / -1 ;
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x = 13 . At this point, the only answer choice that can be correct is answer choice: "[B]: (13, -5)" ; since it is the only answer choice given with a solution of x = 13;
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Nonetheless, we shall continue.
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Now that we have the solution for "x"; "x = 13"; We shall plug this value into, or "SUBSTITUTE" this value, "13", for "x", into the first equation given, " y = 8 − x " ; to find the value of "y" ; as follows:
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y = 8 − x ;
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y = 8 − 13 ;
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y = -5 .
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So, we have x = 13; and y = -5; or write as: (13, -5) . This solution corresponds directly which answer choice: [B]:
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Also, to confirm, let us plug in our solved value for "y", which is "-5" ; into our second equation, to see if the equation holds true:
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7 = 2 − y ;
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7 =? 2 − (-5) ?? ;
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7 =? 2 + 5 ? ? Yes !
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Answer:
The function is defined as H (t) = 4 cos (2π/5 ( t - 1.5)) + 8
Step-by-step explanation:
Solution
Let the function be a cosine function
H(t) a cos(b(t+c)) + d
Now,
The maximum height,is H max =12
The minimum height , is H min = 4
The amplitude, a is denoted by
:
a= H max - H min/2
= 12 - 4/2 = 8/2 = 4
Thus,
The vertical shift , d is given by:
d = H max + H min/2
= 12 + 4 /2 = 16/2 = 8
The period T is given by,
T=6.5-1.5=5
So,
b is given by ,
b= 2π /T = 2π/5
The phase shift , c is given by
:
since maximum height occur at 1.5 we get, c=-1.5
Therefore, our function is defined as:
H (t) = 4 cos (2π/5 ( t - 1.5)) + 8
Answer:
(look in the the Step by step)
Step-by-step explanation:
When the diagonals of a quadrilateral are perpendicular, the area of that quadrilateral is half the product of their lengths.
.. A = (1/2)*d₁*d₂
Substituting the given information, this becomes
.. 58 in² = (1/2)*(14.5 in)*d₂
.. 2*58/14.5 in = d₂ = 8 in
The length of diagonal BD is 8 in.
Answer:
Sarah makes 8 rows of squares.
Step-by-step explanation:
Given:
Number of squares she uses = 48
Number of squares in each row = 6
We need to find the number of rows she can makes.
Solution:
Let the number of rows she can make be 
.
Now we can say that;
Number of rows she can make is equal to Number of squares she uses divided by number of squares in each row.
framing in equation form we get;
Hence Sarah makes 8 rows of squares.
