Question

Let $f$ and $g$ be two real valued functions and $S=\left\{x|f\right(x)=0\}$ and $T=\left\{x|g\right(x)=0\}$, then $S\cap T$ represent the set of roots of

• A. $f\left(x\right)g\left(x\right)=0$
• B. $(f\left(x\right){)}^2+(g\left(x\right){)}^2=0$
• C. $f\left(x\right)+g\left(x\right)=0$
• D. $\frac{f\left(x\right)}{g\left(x\right)}=0$

Answer 1

Answer: (C)

$f\left(x\right)+g\left(x\right)=0$

$f$ and $g$ are two real valued functions.

$S=\{x/f\left(x\right)=0\}$ i.e. roots of $f\left(x\right)=0$ and $T=\{x/g\left(x\right)=0\}\Rightarrow$roots of $g\left(x\right)=0$

$x\in S\cap T\Rightarrow x$ for which $f\left(x\right)$ and $g\left(x\right)$ becomes zero simultaneously.

$\Rightarrow S\cap T$ represents roots of $f\left(x\right)+g\left(x\right)=0$ and $[f\left(x\right){]}^2+[g\left(x\right){]}^2=0$