Question

If f:R->R,f(x)=x-2,g:R->R,g(x)=x+2 then (f+g)(x) =_______
(A)x (B) x2-4 (C) 2x (D)4​

Answer 1

The function $\displaystyle\sf {f:\mathbb{R}\to\mathbb {R}}$ is defined as,

$\displaystyle\longrightarrow\sf{f(x)=x-2}$

The function $\displaystyle\sf {g:\mathbb{R}\to\mathbb {R}}$ is defined as,

$\displaystyle\longrightarrow\sf{g(x)=x+2}$

Then,

$\displaystyle\longrightarrow\sf{(f+g)(x)=f(x)+g(x)}$

$\displaystyle\longrightarrow\sf{(f+g)(x)=x-2+x+2}$

$\displaystyle\longrightarrow\underline {\underline {\sf{(f+g)(x)=2x}}}$

Hence (C) is the answer.

Additional Information:-

For two real functions $\displaystyle\sf {f(x)}$ and $\displaystyle\sf {g(x),}$

• $\displaystyle\sf {(f+g)(x)=f(x)+g(x)}$

• $\displaystyle\sf {(f-g)(x)=f(x)-g(x)}$

• $\displaystyle\sf {(fg)(x)=f(x)\cdot g(x)}$

• $\displaystyle\sf {\left(\dfrac {f}{g}\right) (x)=\dfrac {f(x)}{g(x)},\ g(x)\neq 0}$