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If the function f(x)={{:(k +x, "for " ...

If the function
`f(x)={{:(k +x, "for " x lt1),(4x+3, "for " x ge1):} `
is continuous at `x=1` then `k=`

A

7

B

8

C

6

D

-6

Text Solution

Verified by Experts

f (x) is continuous at `x=1.`
`therefore underset(x to 1)lim f(x) underset(x to 1^(+))lim f(x)=f" "...(1) `
Hence `underset(x to 1 ^(-1))lim (k+x)=underset(x to 1^(+))lim(4x+3)`
`therefore k+1=4(1)+3`
`k=7-1`
`k=6`
Hence, the correct answer from the given alternative is (c ).
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