SOLUTION: F(x)=3x-5 and g(x)=1-x^2 find (FoG)(x) and (GoF)(x) A line passes through the points (7,-3) and (1,3),find the standard form of the line(ax+by=c)

Algebra ->  Equations -> SOLUTION: F(x)=3x-5 and g(x)=1-x^2 find (FoG)(x) and (GoF)(x) A line passes through the points (7,-3) and (1,3),find the standard form of the line(ax+by=c)      Log On


   

Question 154421: F(x)=3x-5 and g(x)=1-x^2
find (FoG)(x) and (GoF)(x)
A line passes through the points (7,-3) and (1,3),find the standard form of the line(ax+by=c)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
(FoG)(x)=f(g(x))=3(1-x^2)-5=3-3x^2-5=-3x^2-2


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(GoF)(x)=g(f(x))=1-(3x-5)^2=1-(9x^2-30x+25)=1-9x^2+30x-25=-9x^2+30x-24


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First let's find the slope of the line through the points and


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%283--3%29%2F%281-7%29 Plug in y%5B2%5D=3, y%5B1%5D=-3, x%5B2%5D=1, and x%5B1%5D=7


m=%286%29%2F%281-7%29 Subtract -3 from 3 to get 6


m=%286%29%2F%28-6%29 Subtract 7 from 1 to get -6


m=-1 Reduce


So the slope of the line that goes through the points and is m=-1


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y--3=-1%28x-7%29 Plug in m=-1, x%5B1%5D=7, and y%5B1%5D=-3


y%2B3=-1%28x-7%29 Rewrite y--3 as y%2B3


y%2B3=-1x%2B-1%28-7%29 Distribute


y%2B3=-1x%2B7 Multiply


y%2B3=-x%2B7 Simplify


y%2B3%2Bx=7 Add "x" to both sides.


y%2Bx=7-3 Subtract 3 from both sides.


x%2By=4 Rearrange and combine like terms


So the equation of the line that goes through the points (7,-3) and (1,3) is x%2By=4