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F(x)=3x-1 and g(x)=x(x-1) then g(f^-1(x)) is ;??? a) (x/3)(x+1) b) (x/3)(x-1) c) 3x(3x-1) d) (x/3)(x/3 +1) F(x)=3x-1 and g(x)=x(x-1) then g(f^-1(x)) is ;??? a) (x/3)(x+1) b) (x/3)(x-1) c) 3x(3x-1) d) (x/3)(x/3 +1)
f(x)=y=3x-1switching the variables to find the inverse function;x=3y-1y=(x+1)/3thus f-¹(x)=(x+1)/3g(f-¹(x))=f-¹(x)(f-¹(x)-1)=((x+1)/3)*((x+1)/3)-1)= ((x+1)/3)*((x+1–3)/3)= ((x+1)(x-2))/9= (x^2 - x - 2)/9
f(x)=y=3x-1
switching the variables to find the inverse function;
x=3y-1
y=(x+1)/3
thus f-¹(x)=(x+1)/3
g(f-¹(x))=f-¹(x)(f-¹(x)-1)
=((x+1)/3)*((x+1)/3)-1)
= ((x+1)/3)*((x+1–3)/3)
= ((x+1)(x-2))/9
= (x^2 - x - 2)/9
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