Mathematics: Find the arithmetic combination of f(x) =x+2, g(x)=x-2

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Find the arithmetic combination of f(x) =x+2,

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krystalhurst97

06.01.2022

The arithmetic combinations of given functions are (f + g)(x) = 2x, (f - g)(x) = 4, (f $\times$ g)(x) = $\mathrm{x}^{2}-4$ , $\left(\frac{f}{g}\right)(\mathrm{x})=\frac{x+2}{x-2}$

Solution:

Given, two functions are f(x) = x + 2 and g(x) = x – 2

We need to find the arithmetic combinations of given two functions .

Arithmetic functions of f(x) and g(x) are (f + g)(x), (f – g)(x), (f $\times$ g)(x), $\left(\frac{f}{g}\right)(\mathrm{x})$

Now, (f + g)(x) = f(x) + g(x)

= x + 2 +x – 2

= 2x

Therefore (f + g)(x) = 2x

similarly,

(f - g)(x) = f(x) - g(x)

= x + 2 –(x – 2)

= x + 2 –x + 2

= 4

Therefore (f - g)(x) = 4

similarly,

(f $\times$ g)(x) = f(x) $\times$ g(x)

= (x + 2) $\times$ (x – 2)

= x $\times$ (x – 2) + 2 $\times$ (x -2)

$=x^{2}-2 x+2 x-4$

$=x^{2}-4$

Therefore (f $\times$ g)(x) = $x^{2}-4$

now,

$\left(\frac{f}{g}\right)(\mathrm{x})=\frac{f(x)}{g(x)}$

$=\frac{x+2}{x-2}$

$(\frac{f}{g})(x)$ = $\frac{x+2}{x-2}$

Hence arithmetic combinations of given functions are (f + g)(x) = 2x, (f - g)(x) = 4, (f $\times$ g)(x) = $\mathrm{x}^{2}-4$ , $\left(\frac{f}{g}\right)(\mathrm{x})=\frac{x+2}{x-2}$

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Find the arithmetic combination of f(x) =x+2, g(x)=x-2

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