Question

What is the inverse of the function f(x) = 2x + 1?

Answer 1

Answer:

$\large\boxed{f^{-1}(x)=\dfrac{1}{2}x-\dfrac{1}{2}}$

Step-by-step explanation:

$f(x)=2x+1\to y=2x+1\\\\\text{exchange x to y and vice versa:}\\\\x=2y+1\\\\\text{solve for y:}\\\\2y+1=x\qquad\text{subtract 1 from both sides}\\\\2y=x-1\qquad\text{divide both sides by 2}\\\\y=\dfrac{x-1}{2}=\dfrac{1}{2}x-\dfrac{1}{2}$