What is f^-1(x) when f(x) = √2x + 3

Question

Solve for f^-1(x) when f(x) = √2x + 3

Answer 1

y = (sqr2)x +3

or y= sqr(2x) + 3?

or y = sqr(2x+3)?

3 different answers depending on which of the above was intended.

try the 1st first

switch x and y and solve for the new y

x = (sqr2)y + 3

x-3 = ysqr2

y = f^-1(x) = (x-3)/sqr2

try the 2nd interpretation of the problem

y = sqr(2x) + 3

switch x and y

x = sqr(2y) +3

x-3 = sqr(2y)

square both sides

2y = (x-3)^2

y = f^-1(x) = [x-3)^2]/2

try the 3rd interpretation

y = sqr(2x +3)

switch x and y

x =sqr(2y +3)

square both sides

x^2 = 2y+3

2y = x^2 -3

y = f^-1(x) = (x^2 -3)/2

f^-1(x) = either (x^2 -3)/2 or [x^2-3)^2]/2 or (x-3)/sqr2

depending on how you interpret the question

Odds are (x-3)/sqr2 is the answer you want