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Q.The function f(x) = [ln(1+ax)-ln(1-bx)]/x, not defined at x=0. The value should be assigned to f at x=0, so that it is continuous at x =0, is
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29%
a+b
32%
a-b
19%
b-a
20%
ln a + ln b
Answer: Option (b) gā(0) = cos(log 2)
Explanation:
Given: f(x) = |log 2 ā sinx|
g(x) = f(f(x))
gā(x) = fā(f(x))fā(x)
Hence, gā(0) = fā(f(0))fā(0)
When x tends to 0, log 2 > sinx
Thus, f(x) = log 2 -sinx
fā(x) = -cos x
fā(0) = ā cos 0 = -1
fā(log 2) = ā cos (log 2)
āgā(0) = (-cos(log 2)) (-1) = cos (log 2)
Hence, option (b) gā(0) = cos (log 2) is the correct answer.
Explanation:
Given: f(x) = |log 2 ā sinx|
g(x) = f(f(x))
gā(x) = fā(f(x))fā(x)
Hence, gā(0) = fā(f(0))fā(0)
When x tends to 0, log 2 > sinx
Thus, f(x) = log 2 -sinx
fā(x) = -cos x
fā(0) = ā cos 0 = -1
fā(log 2) = ā cos (log 2)
āgā(0) = (-cos(log 2)) (-1) = cos (log 2)
Hence, option (b) gā(0) = cos (log 2) is the correct answer.
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