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If the function f(x)={(x",","if",x le 1)...

If the function `f(x)={(x",","if",x le 1),(cx+k"," , "if" , 1 lt x lt 4),(-2x",","if", x ge 4):}`
is continuous everywhere, then the values of c and k are repectively

A

`-3,-5`

B

`-3,5`

C

`-3,-4`

D

`-3,4`

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `f(x)={(x",","if",x le 1),(cx+k",","if", 1 lt x lt 4),(-2x",","if", x ge 4):}`
Since, f(x) si continuous everywhere.
`therefore lim_(x to 1) f(x)=f(1) and lim_(x to 4)f(x)=f(4)`
`therefore lim_(x to 1) (cx+k)=1 and lim_(x to 4) (cx+k) =-2xx4`
`rArr c+k=1 and 4c+k= -8`
On solving, we get `c=-3, k =4`
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