Let f : R R be defined by f ( x ) = 3 x - 4 . Then f - 1 ( x ) is given by:

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Solution

Q.
Let $f : R \to R$ be defined by $f (x) = 3 x - 4$ . Then $f^{- 1} (x)$ is given by:

1 $\frac{x + 4}{3}$

2 $\frac{x}{3} - 4$

3 $3 x + 4$

4 None of the above

Ans.
(1)

Ans. $\frac{x + 4}{3}$

Explanation:

   $f (x) = 3 x - 4$

Let    $y = f (x)$

$y = 3 x - 4$

    $y + 4 = 3 x$

      $\frac{y + 4}{3} = x$

Replacing $y$ by $x$ ,

$∴$    $f^{- 1} (x) = \frac{x + 4}{3}$

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