What is the inverse of the function? #g(x)=−4/3x +2#

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Answer 1 · 2017-12-10T17:56:10

#g^-1(x) = -3/4x +3/2#

This is the first selection.

Given:

#g(x)=−4/3x +2#

Substitute #g^-1(x)# for every instance of x:

#g(g^-1(x))=−4/3g^-1(x) +2#

We know that one of the properties of a function and its inverse is, #g(g^-1(x))= x#, therefore, the left side becomes x:

#x=−4/3g^-1(x) +2#

Solve for #g^-1(x)#:

#−4/3g^-1(x) +2 = x#

#−4/3g^-1(x) = x -2#

#g^-1(x) = -3/4x +3/2#

This is the first selection.