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Let f: X rarr Y be a function defined b...

Let `f: X rarr Y` be a function defined by f(x) = a sin ( x +`pi/4`) + c. If f is both one-one and onto, then find the set X and Y

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`f(x)=a sin(x+pi/4)+bcosx+c`
`=(a sinx)/sqrt2+(acosx)/sqrt2+bcosx+c`
`=(asinx)/sqrt2+cosx(a/sqrt2+b)+c`
`r=(a/sqrt2)^2+(a/sqrt2+b)^2=rsin(x+theta)+c`
`Y in[c-r,c+r]`
f(x) is one-one
`r^2=a^2/2+a^2/2+b^2+sqrt2ab`
`r=sqrt(a^2+b^2+sqrt2ab)`
...
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