If f : R→R and F(x) =sin(π{x})X4+3×2+7, Where { } is a fractional part of x , then

# If f : R→R and F(x) =$\frac{\mathrm{sin}\left(\mathrm{\pi }\left\{\mathrm{x}\right\}\right)}{{\mathrm{X}}^{4}+3{\mathrm{x}}^{2}+7}$, Where { } is a fractional part of x , then

1. A

f is injective

2. B

f is not one -one and non -constant

3. C

f is a surjective

4. D

f is a zero function

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### Solution:

f (x) = $\frac{\mathrm{sin}\left(\mathrm{\pi }\left\{\mathrm{x}\right\}\right)}{{\mathrm{X}}^{4}+3{\mathrm{x}}^{2}+7}$
Here , f (1 /2 )= f(-1 /2)
Clearly, f(x) is not one -one and also it is dependent on x.

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