103,810 views
22 votes
22 votes
Use f(x) = 1/2x and f^-1(x) = 2x to solve the problems.

f(2)=
f^-1(1) =
f^-1(F(2)) =

User Mohamed Hamza
by
3.2k points

1 Answer

9 votes
9 votes

Given:

The functions are:


f(x)=(1)/(2)x


f^(-1)(x)=2x

To find:

The values of
f(2),f^(-1)(1),f^(-1)(f(2)).

Solution:

We have,


f(x)=(1)/(2)x ...(i)


f^(-1)(x)=2x ...(ii)

Putting
x=2 in (i), we get


f(2)=(1)/(2)(2)


f(2)=1

Therefore, the value of
f(2) is 1.

Putting
x=1 in (ii), we get


f^(-1)(1)=2(1)


f^(-1)(1)=2

Therefore, the value of
f^(-1)(1) is 2.

Now,


f^(-1)(f(2))=f^(-1)(1)
[\because f(2)=1]


f^(-1)(f(2))=2
[\because f^(-1)(1)=2]

Therefore, the value of
f^(-1)(f(2)) is 2.

User Sean Kilb
by
2.5k points