SOLUTION: a function is given: f(x) = 3x + 12
a. determine the inverse of this function and name it g(x)
b. use composite functions to show that these functions are inverses
c. evaluat
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Question 1020076: a function is given: f(x) = 3x + 12
a. determine the inverse of this function and name it g(x)
b. use composite functions to show that these functions are inverses
c. evaluate f(g(-2)) explain what is the domain
I think that I got A
y = 3x + 12
x = 3y + 12
x-12 = 3y
y= g(x) = (x-12) / 3
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
a function is given: f(x) = 3x + 12
a. determine the inverse of this function and name it g(x)
1st:: Interchange x and y to get x = 3y+12
2nd: Solve for "y":: f^-1(x) = (x-12)/3
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b. use composite functions to show that these functions are inverses
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fof^-1(x) = f[(x-12)/3] = 3[(x-12)/3)]+ 12 = (x-12)=12 = x
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f^-1of(x) = f^[f(x)] = f^-1[3x+12] = [(3x+12-12)/3] = (3x)/3 = x
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c. evaluate f(g(-2)) explain what is the domain
f(g(-2)) = f((-2-12)/3) = f(-14/3) = 3(-14/3)+12 = -2
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Cheers,
Stan H.
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