fx=3ax+b, x 111, x=15ax-2b, x 1 is continuous at x=1, find a and b - Maths - Continuity and Differentiability

Question

f x = 3 a x + b ,     x > 1 11 ,     x = 1 5
a x - 2 b ,     x < 1   i s   c o n t i n u
o u s   a t   x = 1 ,   f i n d   a   a n
d   b

Aarushi Mishra · Accepted Answer

Since fx is continuous at x=1Thereforelimx→1+fx=f1=limx→1-fxfx=3ax+b, x>111, x=15ax-2b, x<1limx→1+fx=f1since for x>1, fx=3ax+blimx→1+3ax+b=113a+b=11_________1limx→1-fx=f1since for x<1, fx=5ax-2blimx→1-5ax-2b=115a-2b=11_________2multiply equation 1 by 2 and add to equation 211a=33a=3b=11-3a=11-3×3=2

f x = 3 a x + b , x > 1 11 , x = 1 5 a x - 2 b , x < 1 i s c o n t i n u o u s a t x = 1 , f i n d a a n d b .

$f (x) = \{\begin{matrix} 3 a x + b, x > 1 \\ 11, x = 1 \\ 5 a x - 2 b, x < 1 \end{matrix} i s c o n t i n u o u s a t x = 1, f i n d a a n d b .$