Question

If f(x)= 2x then f-1(x)=
(The second one is the inverse)

1/2x
Or
x-2

Answer 1

Given :

f(x) = 2x

To find:

${f}^{ - 1} (x)$

Solution :

If a function f(x) is given,

Then to find its inverse, the given steps are to be taken,

So

it is given that function f(x) = 2x.

step 1 : substitute y for function f(x), so

( function f(x) to be taken as an unknown y.)

y = 2x

step 2 : swap for x and y.

(we have to replace each and every x with y and y with x), so

x = 2y

step 3 : solve for y.

(we have to take all the values of y at one side (i.e. LHS) and x and constants at another side (i.e. RHS). )

$\bf \: y = \frac{x}{2}$

step 4 : rewrite y as

${f}^{ - 1} (x)$

replacing y with inverse of function f(x)

Then Inverse of function f(x) = 2x is :

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