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Let g(x) be a function such that g(a+b)=...

Let `g(x)` be a function such that `g(a+b)=g(a)dotg(b)AAa , b in Rdot` If zero is not an element in the range of `g,` then find the value of `g(x)dotg(-x)dot`

Text Solution

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The correct Answer is:
1
`g(a+b)=g(a)*g(b)`
Put `a=b=0. ` Then,
`g(0)=g^(2)(0)=1 " "["as " g(0) ne 0]`
Now, put `a=x, b= -x. ` Then,
`g(0)=g(x)g(-x)=1`
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