How do you find the inverse of #g(x)= log_3(x+2)-6#?

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Answer 1 · 2015-12-03T15:56:02

#g^-1(x)=3^(x+6)-2#

Write as:

#color(white)(xx)y=log_3(z+2)-6#

Switch #x# and #y#.

#color(white)(xx)x=log_3(y+2)-6#

Solve for #y#.

#color(white)(xx)x+6=log_3(y+2)#

#color(white)(xx)3^(x+6)=3^(log_3(y+2))#

#color(white)(xx)3^(x+6)=y+2#

#color(white)(xx)3^(x+6)-2=y#

Rewrite with #g^-1(x)# instead of #y#.

#color(white)(xx)g^-1(x)=3^(x+6)-2#