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# Let F: R → R Be the Signum Function Defined as And G: R → R Be the Greatest Integer Function Given By G(X) = [X], Where [X] is Greatest Integer Less than Or Equal To X. Then Does Fog And Gof Coincide in (0, 1]? - CBSE (Science) Class 12 - Mathematics

#### Question

Let fR → R be the Signum Function defined as

f(x) = {(1,x>0), (0, x =0),(-1, x< 0):}

and gR → be the Greatest Integer Function given by g(x) = [x], where [x] is greatest integer less than or equal to x. Then does fog and gof coincide in (0, 1]?

#### Solution

It is given that,

fR → R is defined as f(x) = {(1,x>0), (0, x =0),(-1, x< 0):}

Also, gR → R is defined as g(x) = [x], where [x] is the greatest integer less than or equal to x.

Now, let x ∈ (0, 1].

Then, we have:

[x] = 1 if x = 1 and [x] = 0 if 0 < x < 1

:. fog(x) = f(g(x)) = f([x]) = {(f(1), "if x = 1"),(f(0), "if x ∈(0,1)"):} = {(1, "if x = 1"), (0, "if x ∈ (0,1)"):}

gof(x) = g(f(x))`

= g(1)       [x > 0]

=  [1] = 1

Thus, when x ∈ (0, 1), we have fog(x) = 0and gof (x) = 1.

Hence, fog and gof do not coincide in (0, 1].

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 1: Relations and Functions
Q: 18 | Page no. 31

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Solution Let F: R → R Be the Signum Function Defined as And G: R → R Be the Greatest Integer Function Given By G(X) = [X], Where [X] is Greatest Integer Less than Or Equal To X. Then Does Fog And Gof Coincide in (0, 1]? Concept: Types of Functions.
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