First slide

Functions (XII)

Question

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

Moderate

A

$\{4\}, \emptyset$
B

$\emptyset, \{- 2\}$
C

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

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

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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