How do you compute (fog) and (gof) if #f(x) = (3x-1) / (2x+5)# and #g(x) =(7x+3) / (3x-1)#?

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Answer 1 · 2016-03-01T11:24:07

#(f o g)(x)=(18x+10)/(29x+1)#

#(g o f)(x)=(27x+8)/(7x-8)#

Given:
#f(x)=(3x-1)/(2x+5)# and #g(x)=(7x+3)/(3x-1)#

Solution for #(f o g)(x)#

#(f o g)(x)=f(g(x))=(3g(x)-1)/(2g(x)+5)=(3*((7x+3)/(3x-1))-1)/(2*((7x+3)/(3x-1))+5)#

#(f o g)(x)=(21x+9-3x+1)/(14x+6+15x-5)=(18x+10)/(29x+1)#

#(f o g)(x)=(18x+10)/(29x+1)#

~~~~~~~~~~~~~~~

Solution for #(g o f)(x)#

#(g o f)(x)=g(f(x))=(7*f(x)+3)/(3*f(x)-1)=(7*(3x-1)/(2x+5)+3)/(3*(3x-1)/(2x+5)-1)#

#(g o f)(x)=(21x-7+6x+15)/(9x-3-2x-5)=(27x+8)/(7x-8)#

#(g o f)(x)=(27x+8)/(7x-8)#

God bless....I hope the explanation is useful..