Question

The value of constant c that makes the function f defined by 

`f(x) = {{:(x^2-c^2; if x < 4),(cx+20  ; if x > 4):}`

continuous for all real numbers is ______.

विकल्प

• −2

• −1

• 0

• 2

Answer 1

The value of constant c that makes the function f defined by 

`f(x) = {{:(x^2-c^2; if x < 4),(cx+20  ; if x > 4):}`

continuous for all real numbers is −2.

Explanation:

L.H.L. `= lim_(x->4^-) f(x)`

= `lim_(h->0) f(4-h)`

= `lim_(h->0) (4-h)^2 - c^2`

= (4 - 0)² − c²

= 16 − c²

R.H.L. `= lim_(x->4^+) f(x)`

= `lim_(h->0) f(4+h)`

= `lim_(h->0) c(4+h)+20`

= c(4 + 0) + 20

= 4c + 20

Given function is continuous, Then

L.H.L. = R.H.L.

16 − c² = 4c + 20

c² + 4c + 4 = 0

(c + 2)² = 0

c + 2 = 0

c = −2