Find the inverse function of f informally Fx 2x f1x Verify

Find the inverse function of f informally. F(x) = 2x f^-1(x) = Verify that f(f^-1(x)) = x and f^-1(f(x)) = x. F(f^-1(x)) = f () = 2 () = x f^-1(f(x)) = f^-1() = 2x/= x

Solution

Solution:

f(x) = 2x

y= 2x

swtich y and x

x = 2y

y = x/2

f^-1(x) = x/2

Now

f(f^-1(x)) = f(x/2) ....x = f^-1(x)  ( Answer1 )

= 2 (x/2) .... Answer 2

= x

Similerly

f^-1(f(x)) = f^-1(2x) ... f(x) = 2x Answer 3

= 2x/2     Answer 4 f^-1(x) = x/2

= x

  

Answer