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

1 Answer
Nov 25, 2015

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

Explanation:

[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)