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If f(x)={(log((1-3x))(1+3x)",","for",x n...

If `f(x)={(log_((1-3x))(1+3x)",","for",x ne 0),(k",","for",x =0):}` is continuous at x = 0, then k is equal to

A

`-2`

B

2

C

1

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `f(x)=k{(log_((1-3x))(1+3x)",","for "x ne 0),(k",", "for "x=0):}`
Now, `lim_(x to 0) f(x)=lim_(x to 0) (log(1+3x))/(log(1-3x)) " "[because log_(b)a=(log a)/(log b)]`
`=-lim_(x to 0)(log(1+3x))/(3x)*((-3x))/(log(1-3x))=-1`
`and f(0)=k`
`because ` f(x) is continuous at x = 0.
`therefore k = -1 `
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