If f:R→ R is given by f(x)= beginmatrix -1, when x is rational 1, when x is irrational endmatrix . then (fof) (1-√3) is equal to

Question

If f:R→ R is given by f(x)= beginmatrix -1, when x is rational 1, when x is irrational endmatrix . then (fof) (1-√3) is equal to (A)  1  (B)  -1  (C)  √3  (D)  0

Tardigrade Admin · Accepted Answer

Given, f(x)= beginmatrix -1, where x is rational 1, when x is irrational endmatrix . Now, (fof) (1-√3)=f[f(1-√3)]=f(1)=-1

Q. If $f : R \to R$ is given by
$f (x) = {- 1, w h e n x i s r a t i o na l 1, w h e n x i s i rr a t i o na l$
then $(f o f) (1 - 3)$ is equal to

$1$

$- 1$

$3$

$0$

Given, $f (x) = {- 1, w h ere x i s r a t i o na l 1, w h e n x i s i rr a t i o na l$
Now, $(f o f) (1 - 3) = f [f (1 - 3)] = f (1) = - 1$

Q. If f:R→R is given by f(x)={−1,whenxisrational1,whenxisirrational​ then (fof)(1−3​) is equal to

1

−1

3​

0

Given, f(x)={−1,wherexisrational1,whenxisirrational​ Now, (fof)(1−3​)=f[f(1−3​)]=f(1)=−1

Q. If $f : R \to R$ is given by
$f (x) = {- 1, w h e n x i s r a t i o na l 1, w h e n x i s i rr a t i o na l$
then $(f o f) (1 - 3)$ is equal to

$1$

$- 1$

$3$

$0$

Given, $f (x) = {- 1, w h ere x i s r a t i o na l 1, w h e n x i s i rr a t i o na l$
Now, $(f o f) (1 - 3) = f [f (1 - 3)] = f (1) = - 1$