Inverse of f(x)=2x+1/3?

Question

whats the inverse of the function please help

Answer 1

inverse of f(x)=x/2 -1/6

switch the values of x and y

F(x) is the same as y

Answer 2

Take the equation

y = 2x + 1/3

Solve for x

y - 1/3 = 2x

(1/2)y - 1/6 = x

So...

f-1(x) = (1/2)x - 1/6

Answer 3

First write f(x)=2x+1/3 as y = 2x+1/3

Next swap x and y

y = 2x + 1/3 becomes

x = 2y + 1/3

Now solve for y

x = 2y + 1/3

2y = x - 1/3

y = x/2 - 1/6

Answer:  f⁻¹(x) = x/2 - 1/6

Another way to do this is use definition of inverse, i.e.

f( f⁻¹(x)) = x ---> replace x with f⁻¹(x) in original function

2 f⁻¹(x) + 1/3 = x

2 f⁻¹(x) = x - 1/3

f⁻¹(x) = x/2 - 1/6