Let $g(x) =1+ x −[x]$ and $f (x) =

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

Let $g(x) =1+ x −[x]$ and $f (x) = sgn(x)$. Then for all x, $f\{g(x)\}$ is equal t

Options:

$x$

$f(x)$

$g(x)$

Correct Answer:

Explanation:

$∴g(x)=1+x-[x]=1+\{x\}≥1\,∀\,x∈R$

by definition of $f(x)=1,x>0$

$f(g(x)≥1)=1$