How do you find the inverse of #y= 2^(1.5x+3)#?

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Answer 1 · 2015-11-25T13:20:08

#f^-1(x)=(log_2x-3)/1.5#

#[1]" "f(x)=2^(1.5x+3)#

#[2]" "y=2^(1.5x+3)#

Switch #x# and #y#.

#[3]" "x=2^(1.5y+3)#

Convert this to logarithmic form.

#[4]" "hArrlog_2x=1.5y+3#

Subtract 3 from both sides.

#[5]" "log_2x-3=1.5y#

Divide both sides by #1.5#.

#[6]" "(log_2x-3)/1.5=y#

#[7]" "color(blue)(f^-1(x)=(log_2x-3)/1.5)#