Solve 10 and 12: 10 f(x) = x+1, ifx≥1x2+1, ifx 1 12 f(x) - Maths - Continuity and Differentiability

Question

Solve 10 and 12:
10     f ( x )   =   x + 1 ,     i f
x ≥ 1 x 2 + 1 ,     i f x < 1

12   f ( x )   =   x 10 - 1 , i f   x  
≤ 1 x 2 , i f   x   > 1

Aarushi Mishra · Accepted Answer

Dear studentI am assuming that you are asking to check continuityFor fx to be continuous at x=a, limx→a+fx=limx→a-fx=fafx=x+1, if x≥1x2+1, if x<1f1=1+1=2limx→1+fx=limx→1+x+1  for x≥1, fx=x+1=1+1=2limx→1-fx=limx→1-x2+1  for x<1, fx=x2+1=12+1=2Thereforelimx→1-fx=limx→1+fx=f1=2Hence fx is continuousFor remaining queries please post them in a new thread

Solve 10 and 12: 10 . f ( x ) = x + 1 , i f x ≥ 1 x 2 + 1 , i f x < 1 12 . f ( x ) = x 10 - 1 , i f x ≤ 1 x 2 , i f x > 1

Solve 10 and 12:
$10 . f (x) = (\begin{matrix} x + 1, i f & x \geq 1 \\ x^{2} + 1, i f & x < 1 \end{matrix})$

$12 . f (x) = (\begin{matrix} x^{10} - 1, & i f x \leq 1 \\ x^{2}, & i f x > 1 \end{matrix})$