A) The domain remains the same.
Since, in y = - 2 f(x) , the y is whats being multiplied and therefore changed, not the x or domain.
Therefore D[-6,10] <span>
The range is what changes by a factor of -2.
If the original range was [-8,12], then the new one is
[(-8 x -2),(12 x -2)] = [16 , -24].
However, you must flip the numbers to make the interval true, giving you R [-24,16]</span>
L1: 2x+4y-3=0 ..........(1)
P: (2,0)
The point on the line L1 closest to the given point P is at the intersection of L1 with L2, which is the perpendicular passing through P.
Slope of L1=-2/4=-1/2
Slope of L2=-1/(-1/2)=2
Since it passes throug P(2,0), we can use the point-slope formula:
(y-0)=2(x-2) =>
L2: 2x-y-4=0.............(2)
Solve for x & y using (1) and (2) to get intersection point required:
(1)-(2)
2x-2x + 4y-(-y) -3 -(-4) =0
5y=-1, y=-1/5
Substitute y=1/5 in equation (1)
2x+4(-1/5)-3=0 =>
2x-19/5=0
x=19/10
=> the point on L1 closest to (2,0) is (19/10, -1/5)
Answer:
S+L=6
10S+18L=76
Step-by-step explanation:
S for small
L for larger
