A) 4
B) 3
C) 5
D) 2
Correct Answer: B
Solution :
\[f(xy)=f(x).f(y)\] |
\[f(0)=1\]as \[f(0)\ \ne 0\] |
\[\Rightarrow \] \[f(x)=1\] |
\[\frac{dy}{dx}=f(x)=1\] |
\[\Rightarrow \] \[y=x+c\] |
At, \[x=0,\text{ }y=1\] |
\[\Rightarrow \] \[c=1\] |
\[y=x+1\] |
\[\Rightarrow \] \[y\left( \frac{1}{4} \right)+y\left( \frac{3}{4} \right)=\frac{1}{4}+1+\frac{3}{4}+1=3\] |
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