If the function f(x) = begincases a | π - x | + 1 , x le 5 b | x - π | + 3 , x 5 endcases is continuous at x = 5, then the value of a - b is :-

Question

If the function f(x) = begincases a | π - x | + 1 , x le 5 b | x - π | + 3 , x > 5 endcases is continuous at x = 5, then the value of a - b is :- (A) (2/5-π)  (B) (2/π - 5 )  (C) (2/π + 5 )  (D) ( - 2/π + 5 )

Tardigrade Admin · Accepted Answer

a|π-5|+1 = b |5-π| +3 a(5-π)+1 =b(5-π)+3 (a -b)(5-π) = 2 a-b = (2/5-π)

Q. If the function $f (x) = {a ∣ π - x ∣ + 1, x \leq 5 b ∣ x - π ∣ + 3, x > 5$ is continuous at x = 5, then the value of a - b is :-

$\frac{2}{5 - π}$

$\frac{2}{π - 5}$

$\frac{2}{π + 5}$

$\frac{- 2}{π + 5}$

$a ∣ π - 5 ∣ + 1 = b ∣ 5 - π ∣ + 3$
$a (5 - π) + 1 = b (5 - π) + 3$
$(a - b) (5 - π) = 2$
$a - b = \frac{2}{5 - π}$

Q. If the function f(x)={a∣π−x∣+1,x≤5b∣x−π∣+3,x>5​ is continuous at x = 5, then the value of a - b is :-

5−π2​

π−52​

π+52​

π+5−2​