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f(x) Transforms to f(x+a) or f(x-a)

If gx is shif...

Question

If $g (x)$ is shifted $1$ unit left of $f (x) = x^{2} - 6,$ then $g (x)$ is

A

x^{2} - 7

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B

x^{2} - 5

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C

x^{2} + 2 x - 5

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D

x^{2} - 2 x - 5

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Solution

The correct option is C $x^{2} + 2 x - 5$
As $g (x)$ is shifted $1$ unit left of $f (x)$ , so
$g (x) = f (x + 1) \Rightarrow g (x) = {(x + 1)}^{2} - 6 \Rightarrow g (x) = x^{2} + 2 x + 1 - 6 ∴ g (x) = x^{2} + 2 x - 5$

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f(x) Transforms to f(x+a) or f(x-a)

Standard XII Mathematics

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