Question

Find the invers of f(x)=4/2x+1​

Answer 1

`\boxed{\pink{\sf The \ inverse\ of \ the \ function \ is \ f^(-1)(x)= (2)/(x)-(1)/(2) }}`

Explanation:

A function is given to us and we need to find its inverse . So the given function is ,

`\implies f(x) = (4)/(2x+1)`

1) So ,let us take f(x) = y . Equation becomes ,

`\implies y = (4)/(2x+1)`

2) Firstly replace x with y and y with x. We get ,

`\implies x = (4)/(2y+1)`

3) Now , solve for y.

`\implies x = (4)/(2y+1) \\\\\implies x(2y + 1) = 4 \\\\\implies 2y+1 =(4)/(x)\\\\\implies 2y = (4)/(x)-1 \\\\\implies 2y = (4-x)/(x) \\\\\implies y = (4-x)/(2x)`

4) Now replace y with
`f^(-1)(x)`

`\implies f^(-1)(x) = (4-x)/(2x) \\\\\ \implies f^(-1)(x)= (4)/(2x) - (x)/(2x) \\\\\underline{\boxed{\orange{\tt \implies f^(-1)(x) = (2)/(x)-(1)/(2) }}}`