Consider r(x) = (2x-7) / (4x-6)
a)Find and simplify: r(r(x))
b) Find and simplify: r^-1(x)
c) Verify that r(r(x)) = r^-1(x)
Please help me. I am really stuck and I can't find help any other way. Please & Thank you! Please.
a)Find and simplify: r(r(x))
b) Find and simplify: r^-1(x)
c) Verify that r(r(x)) = r^-1(x)
Please help me. I am really stuck and I can't find help any other way. Please & Thank you! Please.
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Consider r(x) = (2x-7) / (4x-6)
a)Find and simplify: r(r(x))
plug r(x) in for x:
= {2[(2x-7)/(4x-6)] -7} / {4[(2x-7)/(4x-6)] -6}
= multiply by (4x-6)/(4x-6)
=[ (4x-14)-7(4x-6)]/[(8x-28)-6(4x-6)]
= (-24x+28)/(-16x+8)
= -4(6x-7)/-4(4x-2)
= (6x-7)/(4x-2)
B) let x= (2y-7)/(4y-6)= (1/2)-4/( 4y -6). By long division
X-1/2= -4/(4y-6)
4y-6= -4/( x-1/2)= -8/( 2x-1)
4y = 6-8/(2x-1)= (12x-14)/(2x-1)
Y= 2(6x-7)/4(2x-1)
r^-1(x)= (6x-7)/(4x-2)
C)they are the same!
Hoping this helps!
a)Find and simplify: r(r(x))
plug r(x) in for x:
= {2[(2x-7)/(4x-6)] -7} / {4[(2x-7)/(4x-6)] -6}
= multiply by (4x-6)/(4x-6)
=[ (4x-14)-7(4x-6)]/[(8x-28)-6(4x-6)]
= (-24x+28)/(-16x+8)
= -4(6x-7)/-4(4x-2)
= (6x-7)/(4x-2)
B) let x= (2y-7)/(4y-6)= (1/2)-4/( 4y -6). By long division
X-1/2= -4/(4y-6)
4y-6= -4/( x-1/2)= -8/( 2x-1)
4y = 6-8/(2x-1)= (12x-14)/(2x-1)
Y= 2(6x-7)/4(2x-1)
r^-1(x)= (6x-7)/(4x-2)
C)they are the same!
Hoping this helps!