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Composite Function

If fx=x, gx...

Question

If $f (x) = x, g (x) = 2 x^{2} + 1$ and $h (x) = x + 1$ then $(h o g o f) (x)$ is equal to

x^{2} + 2

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2 x^{2} + 1

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x^{2} + 1

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2 (x^{2} + 1)

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Solution

The correct option is D $2 (x^{2} + 1)$
Given $f (x) = x, g (x) = 2 x^{2} + 1$ and $h (x) = x + 1$

$h o g o f (x)$

$= h (g (f (x)))$
$= h (g (x)) \dots \dots [∵ f (x) = x]$
$= h (2 x^{2} + 1) \dots \dots [∵ g (x) = 2 x^{2} + 1]$
$= 2 x^{2} + 1 + 1$
$= 2 x^{2} + 2$
$= 2 (x^{2} + 1)$
$∴ h o g o f (x) = 2 (x^{2} + 1)$

Suggest Corrections

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\frac{1}{2} (g \circ f) (x) = 2 x^{2} - 5 x + 2

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g (x) = x^{2} + x - 2 and \frac{1}{2} g o f (x) = 2 x^{2} - 5 x + 2

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^{2}

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f (x) = x + 2; g (x) = x; h (x) = x^{2}

h o (g o f) (x) =

2 x^{2} - 5 x + 1

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