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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`) + b cosx + c. If f is both one-one and onto, then find the set X and Y

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The correct Answer is:
`X in [-pi/2-alpha,pi/2-alpha] " and " Y in [c-r,c+r], " where " alpha=tan^(-1)((alpha+bsqrt(2))/a) " and " r=sqrt(a^(2)+sqrt(2)ab+b^(2))`
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