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Why can a variable be used to represent a number

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If, g(x)=-2(x+2)-6 what is g(b-5)=

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<u>Solution:</u>

In the notation g(x) we know that whatever is put in the parentheses is what we replace for x. In the given situation, since it is g(b-5) we have to replace every x in the function with b-5. That is if,

$g(x)=-2(x+2)-6$

then, $g(b-5)=-2((b-5)+2)-6$

$\Rightarrow g(b-5)=-2(b-5+2)-6$

On solving we get,

$\Rightarrow g(b-5)=-2(b-3)-6\rightarrow g(b-5)=-2b+6-6$

$\Rightarrow g(b-5)=-2b$

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