Question

Find the inverse of f(x)=2x-1

Answer 1

${ \qquad\qquad\huge\underline{{\sf Answer}}}$

Let's find the inverse of given function ~

$\qquad \sf \dashrightarrow \: f(x) = 2x - 1$

$\qquad \sf \dashrightarrow \: 2x = f(x) + 1$

$\qquad \sf \dashrightarrow \: x = \cfrac{f(x) + 1}{2}$

[ now, replace f(x) and x with $\sf{ {f}^{-1}(x)}$ ]

$\qquad \sf \dashrightarrow \: f {}^{ - 1} (x) = \cfrac{x + 1}{2}$

That's the required inverse function ~

Answer 2

Answer:

$\frac{x+1}{2}$

Step-by-step explanation:

The inverse of a function $f(x)$ is denoted by f$^{-1}(x)$

To find the inverse of $f(x) = 2x -1$

Set $y = f(x)$

So

$y = 2x-1$

Express x in terms of y

$y+1 = 2x \textrm{ or } 2x = y + 1$

$x=\frac{y+1}{2}$

So inverse is $f^{-1}(x) =$ $\frac{x+1}{2}$

Replace y with x to make it a function of x

$f^{-1}(x) =$ $\frac{x+1}{2}$

To test if this correct, note that the property of an inverse function is that it undoes the original function. In other words if we have f(a) = k then f⁻¹(k) = a

Let's test this with some reasonable value for x

f(2) = 2.2 - 1 = 3

f⁻¹(3) = (3+1)/2 = 2

Hence correct