SOLUTION: Determine whether the following pairs are invers of eachother a. f9x0=8x-7 and g(x)=x+8/7 b. f(x)= 1/x and g(x)= 1/x c. f(x)= 2x+3/x-1 and g(x)=x+3/x-2

Question 134933: Determine whether the following pairs are invers of eachother
a. f9x0=8x-7 and g(x)=x+8/7
b. f(x)= 1/x and g(x)= 1/x
c. f(x)= 2x+3/x-1 and g(x)=x+3/x-2
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Determine whether the following pairs are invers of eachother
a. f(x)=8x-7 and g(x)=(x+8)/7
fog(x)= f[(x+8)/7] = 8[(x+8)/7]
They are not inverse as the result has to be "x" if f and g are inverse.
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b. f(x)= 1/x and g(x)= 1/x
fog(x) = f(1/x) = 1/(1/x) = x
gof(x) = g(1/x) = 1/(1/x) = x
There are inverse to one another.
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c. f(x)= 2x+3/x-1 and g(x)=x+3/x-2
fog(x) = f[(x+3)/(x-2)] = [2[(x+3)/(x-2)]+3]/[(x+3)/(x-2)-1]
= [(2x+6)+3(x-2)]/(x-2) / [(x+3 -x+2]/(x-2)
= [2x+6 + 3x-6]/[5]
= [5x]/5 = x
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If you have the patience, check gof(x) to see if you "x"
If you do, f and g are inverse.
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Cheers,
Stan H.

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