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If $f : R \to R$ is defined by $f (x) = x^{2} + 1$ then value of $f^{- 1} (17)$ and $f^{- 1} (- 3)$ are, respectively.

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ϕ,{4,−4}

ϕ, {3,−3}

{{3,−3}, ϕ

{4,−4}, ϕ

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detailed solution

Correct option is D

For any A⊆R, we have f−1(A)={x∈R:f(x)∈A}. Thus, f−1(17)={x:f(x)∈{17}}={x:f(x)=17}=x:x2+1=17={4,−4}.and similarly, ∣f−1(−3)=x∈R:x2+1=−3=ϕ

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If f:R→R is defined by f(x)=x2+1 then value of f−1(17) and f−1(−3) are, respectively.

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If $f : R \to R$ is defined by $f (x) = x^{2} + 1$ then value of $f^{- 1} (17)$ and $f^{- 1} (- 3)$ are, respectively.