If #g( x ) = \frac { 2x - 7} { 3x }#, what is #g^-1(x)#?

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Answer 1 · 2016-12-22T06:42:39

The answer is #" "g^-1(x)=7/(2-3x)#

Let #y=(2x-7)/(3x)#

#3xy=2x-7#

#2x-3xy=7#

#x(2-3y)=7#

#x=7/(2-3y)#

Therefore,

#g^(-1)(x)=7/(2-3x)#

Verification

#g(g^(-1)(x))=g(7/(2-3x))=(2*7/(2-3x)-7)/(3*7/(2-3x))#

#=(14-7(2-3x))/(21)#

#=(21x)/21=x#

#:.x = x#