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RideAnS [48]
3 years ago
13

Let f(x) = -2x + 7 and g(x) = -6x + 3. Find (f o g) and state its domain.

Mathematics
1 answer:
Vladimir79 [104]3 years ago
3 0

(f\circ g)(x) = -2(-6x+3) + 7 = 12x - 6 + 7 = 12x + 1

The domain is all real numbers as a composition of two linear functions have no restrictions (all linear functions have domain of R)

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1368⁄75 is approximately equal to what value
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2 years ago
Compare the line passing through the points (−3, −11) and (6, 4) to the line given by the equation y=35x−6.
Aleks04 [339]
Let
<span>A------> (−3, −11)
B------>  (6, 4)

step 1
find the slope m point A and point B
m=(y2-y1)/(x2-x1)-----> </span>m=(4+11)/(6+3)----> m=15/9---> 5/3

step 2
with m=5/3 and point B (6, 4)  find the equation of a line
y-y1=m*(x-x1)-----> y-4=(5/3)*(x-6)---> y=(5/3)x-6

case <span>a. they have the same slope------> is not correct
because
</span><span>y=35x−6------> the slope m=35
</span>y=(5/3)x-6---> the slope m =5/3

case <span>b. they have the same x-intercept.----> is not correct
because
</span>the x-intercept is for y=0

y=35x−6-----> 0=35x-6----> 35x=6-----> x=6/35
the x-intercept is the point (6/35,0)

y=(5/3)x-6----> 0=(5/3)x-6----> (5/3)x=6---> x=18/5
the x-intercept is the point (18/5,0)

case <span>c. the two lines are perpendicular. do. they have the same y-intercept-----> is nor correct
because

if two lines are perpendicular
m1*m2=-1-------> </span><span>this condition is not satisfied
</span>
the y intercept is for x=0

y=35x−6-------> y=-6
the y intercept is the point (0,-6)

y=(5/3)x-6-----> y=-6
the y intercept is the point (0,-6)

 they have the same y-intercept but the two lines are not perpendicular

see the attached figure

7 0
3 years ago
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