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Q.

If f:R→R defined by f(x)=x4+2 then the value of f-1(83) and f-1(-2) respectively are

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a

∅,{3,–3}

b

{3,–3},∅

c

{4,–4},∅

d

{4,–4},{2,-2}

answer is B.

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Detailed Solution

f(x)=x4+2 =y⇒ x=y–21/4⇒ f-1(x)=(x-2)1/4⇒ f-1(83)=(81)1/4=±3and  f-1(-2)=(-4)1/4=∅.
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If f:R→R defined by f(x)=x4+2 then the value of f-1(83) and f-1(-2) respectively are