If f : R→ R, defined by f (x) = x3 + 7, then the value of f –1(71) and f –1 (–1) respectively are

f (x) = x3+ 7 = 71 ⇒ x3 = 64 ⇒ x = 4⇒ f-1(71)=4and f(x)=x3+7=–1⇒x3=–8⇒x=–2⇒f-1(–1)=–2

If f : R→ R, defined by f (x) = x3 + 7, then the value of f –1(71) and f –1 (–1) respectively are

f (x) = x3+ 7 = 71 ⇒ x3 = 64 ⇒ x = 4⇒ f-1(71)=4and f(x)=x3+7=–1⇒x3=–8⇒x=–2⇒f-1(–1)=–2

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If $f : R \to R$ , defined by f (x) = x³ + 7, then the value of f ^–1(71) and f ^–1 (–1) respectively are

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$\{4\}, \emptyset$

$\emptyset, \{- 2\}$

$\{4\}, \{- 2\}$

$\{2\}, \{- 4\}$

answer is C.

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Detailed Solution

$f (x) = x^{3} + 7 = 71 \Rightarrow x^{3} = 64 \Rightarrow x = 4$

$\Rightarrow f^{- 1} (71) = \{4\}$

and $f (x) = x 3 + 7 = - 1 \Rightarrow x 3 = - 8 \Rightarrow x = - 2 \Rightarrow f^{- 1} (- 1) = - 2$

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If f : R→ R, defined by f (x) = x3 + 7, then the value of f –1(71) and f –1 (–1) respectively are

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If $f : R \to R$ , defined by f (x) = x³ + 7, then the value of f ^–1(71) and f ^–1 (–1) respectively are