If f(x)= ll x+a, & x 0 |x-4|, & x>0 . and g(x)= ll x+1 & x<0 (x-4… - Vidyadip

MCQ

If $f(x)=\left\{\begin{array}{ll}x+a, & x \leq 0 \\ |x-4|, & x>0\end{array}\right.$ and $g(x)=\left\{\begin{array}{ll}x+1 & x<0 \\ (x-4)^{2}+b, & x \geq 0\end{array}\right.$ are continuous on $R$, then $(\text{gof}) (2)+( \text{fog}) (-2)$ is equal to.

A
$-10$
B
$10$
C
$8$
✓
$-8$

✓

Answer

Correct option: D.

$-8$

$(x)=\left\{\begin{array}{l} x+a ; x \leq 0 \\ |x-4| ; x>0 \end{array} ; g(x)=\left\{\begin{array}{ll} x+1 & ; x<0 \\ (x-4)^{2}+b ; & x \geq 0 \end{array}\right.\right.$
For continuity $a =4$ and $b =-15$
$g(f(2))+f(g(-2))$
$=g(2)+f(-1)=-8$

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