What is the inverse of #g(x)=(x+8)/3#?

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Answer 1 · 2017-01-14T22:20:15

#g^-1(x) = 3x - 8#

Let #y = g(x)#. So,

#y = (x+8)/3#

#3y = x + 8#

#x = 3y - 8#

#g^-1(y) = 3y - 8#.

Therefore,

#g^-1(x) = 3x - 8#

If we wanted, we could first prove that #g# is invertible, by showing that for any #x_1,x_2inA#, where #A# is the domain of #g#, #g(x_1)=g(x_2)#

#x_1 = x_2#, so #x_1 + 8 = x_2 + 8# and #(x_1 + 8)/3 = (x_2 + 8)/3#

It holds that if #x_1 = x_2#, #g(x_1) = g(x_2)#.

Thus, #g# is invertible.