Answer:
(a) h(x) = 1/2x -1/2
Step-by-step explanation:
The inverse of the function y = f(x) is found by solving x = f(y).
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<h3>setup</h3>
x = f(y)
x = 2y +1 . . . . . . use the definition of f(x)
<h3>solution</h3>
x -1 = 2y . . . . . subtract 1
(x -1)/2 = y . . . . divide by 2
y = 1/2x -1/2 . . . . eliminate parentheses
h(x) = 1/2x -1/2 . . . write in functional form
The inverse of f(x) = 2x+1 is ...
h(x) = 1/2x -1/2
Because of the symmetry, we can just go from x=0 to x=2 to find the area between
<span>y = x^2 and y = 4 </span>
<span>that area = ∫4-x^2 dx from 0 to 2 </span>
<span>= [4x - (1/3)x^3] from 0 to 2 </span>
<span>= 8 - 8/3 - 0 </span>
<span>= 16/3 </span>
<span>so when y = b </span>
<span>x= √b </span>
<span>and we have the area as </span>
<span>∫(b - x^2) dx from 0 to √b </span>
<span>= [b x - (1/3)x^3] from 0 to √b </span>
<span>= b√b - (1/3)b√b - 0 </span>
<span>(2/3)b√b = 8/3 </span>
<span>b√b =4 </span>
<span>square both sides </span>
<span>b^3 = 16 </span>
<span>b = 16^(1/3) = 2 cuberoot(2) </span>
<span>or appr 2.52</span>
Answer:
1/49
<em>Step by step explanation:</em>
Step-by-step explanation:
If you want the "root" of the equation...
First get y by itself on one side. You should get y = - x - 8.
Notice that this is the equation of a straight line.
Then let y = 0, and solve for x. You should get x = -8.
So the solution or "root" of the equation is at the point (-8,0)
Answer:
Step-by-step explanation:
Subtract 7 from both sides.
Multiply both sides by v.
Multiply both sides by 1/(y - 7).
