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Question

The function 'g' defined by g(x)=sinα+cosα1 where α=sin1{x} is (where {.} denotes fractional part function)

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Solution

g(x)=sinα+cosα1α=sin1{x}
{x}=1{x} from the graph of {x}
0{x}<10{x}<10sin1{x}<π2g(x)=sin(sin1{x})+cos(sin1{x})1={x}+(1{x})1g(x)={x}+(1{x})1=1{x}+{x}1g(x)=g(x)
even function
g(x+T)={x+T}+1{x+T}1
if T is integer
g(x+T)={x}+(1{x})1=g(x)
periodic with integer period
not other wise

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