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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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Answer» `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)` option a is correct. |
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