If f(x)= begincases x+a, x ≤ 0 |x-4|, x0 endcases and g(x)= begincasesx+1 , x

Question

If f(x)= begincases x+a, x ≤ 0 |x-4|, x>0 endcases and g(x)= begincasesx+1 , x<0 (x-4)2+b, x ≥ 0 endcases are continuous on R, then (gof) (2)+(f o g)(-2) is equal to : (A) -10 (B) 10 (C) 8 (D) -8

Tardigrade Admin · Accepted Answer

f(x)= begincasesx+a ; x ≤ 0 |x-4| ; x>0 endcases ; g(x)= begincases x+1 ; x<0 (x-4)2+b ; x ≥ 0 endcases For continuity a=4 and b=-15 g ( f (2))+ f ( g (-2)) = g (2)+ f (-1)=-8

Q. If $f (x) = {x + a, ∣ x - 4∣, x \leq 0 x > 0$ and $g (x) = {x + 1 (x - 4)^{2} + b,, x < 0 x \geq 0$ are continuous on $R$ , then $(g o f) (2) + (f o g) (- 2)$ is equal to :

-10

10

8

-8

$f (x) = {x + a; x \leq 0 ∣ x - 4∣; x > 0; g (x) = {x + 1; x < 0 (x - 4)^{2} + b; x \geq 0$
For continuity $a = 4$ and $b = - 15$
$g (f (2)) + f (g (- 2))$
$= g (2) + f (- 1) = - 8$

Q. If f(x)={x+a,∣x−4∣,​x≤0x>0​ and g(x)={x+1(x−4)2+b,​,x<0x≥0​ are continuous on R, then (gof)(2)+(fog)(−2) is equal to :

-10

10

8

-8

f(x)={x+a;x≤0∣x−4∣;x>0​;g(x)={x+1;x<0(x−4)2+b;x≥0​ For continuity a=4 and b=−15 g(f(2))+f(g(−2)) =g(2)+f(−1)=−8

Q. If $f (x) = {x + a, ∣ x - 4∣, x \leq 0 x > 0$ and $g (x) = {x + 1 (x - 4)^{2} + b,, x < 0 x \geq 0$ are continuous on $R$ , then $(g o f) (2) + (f o g) (- 2)$ is equal to :

$f (x) = {x + a; x \leq 0 ∣ x - 4∣; x > 0; g (x) = {x + 1; x < 0 (x - 4)^{2} + b; x \geq 0$
For continuity $a = 4$ and $b = - 15$
$g (f (2)) + f (g (- 2))$
$= g (2) + f (- 1) = - 8$