find the inverse equation

Question

find the inverse of y= f(t) = √(3t) +2 

f^-1 (y) = 

Answer 1

The best way to find inverse of an equation is by interchanging the independent variable (which in this case is t) and y.  

 

The given function is y=√(3t)+2

 

The inverse function can be obtained by interchanging (switching) t and y

 

t=√(3y)+2

 

subtract 2 from both sides to get t -2 = √(3y)

 

squaring both sides we get (t - 2)² = 3y

 

Dividing both sides by 3 we get y = (t - 2)² /3

 

f(y) = √(3t)+2 (given) and f ^-1(y) = (t - 2)² /3

Answer 2

Switch t and y, and solve for y to get f^-1 (y),

t = √(3y) +2

(t-2)^2 = 3y

 

f^-1 (y) = y = (1/3)(t-2)^2, where t ≥ 2 <==Answer