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Properties of Inverse Function

Let f, g and ...

Question

Let f, g and h be function defined as follows $f (x) = x + 2, g (x) = 3 x - 1, h (x) = 2 x$ , Then $h o (g o f)$

6 x + 10

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3 x - 1

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10 x - 6

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10 x + 6

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Solution

The correct option is A $6 x + 10$
Given $f (x) = x + 2, g (x) = 3 x - 1, h (x) = 2 x$

$g o f = 3 (x + 2) - 1 = 3 x + 5$ , ( $g o f$ is another representation for $g (f (x))$ )

Therefore, $h o (g o f) = 2 (3 x + 5) = 6 x + 10$

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