First slide

Functions (XII)

Question

$If f (x) is an invertible function and g (x) = 2 f (x) + 5, then the value of g^{- 1} (x) is$

Moderate

A

$2 f^{- 1} (x) - 5$
B

$\frac{1}{2 f^{- 1} (x) + 5}$
C

$\frac{1}{2} f^{- 1} (x) + 5$
D

$f^{- 1} (\frac{x - 5}{2})$

Solution

$\begin{aligned} Replacing x by g^{- 1} (x), we get x = 2 f (g^{- 1} (x)) + 5 \\ ∴ f (g^{- 1} (x)) = \frac{x - 5}{2} \\ ∴ g^{- 1} (x) = f^{- 1} (\frac{x - 5}{2}) \end{aligned}$

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