Function Operations

If we imagine the first function as the detergent and the second function as the softener, evaluating a function operation is like doing laundry.

When we evaluate a function operation, we can plug the input into each function separately and then combine their outputs using the given operation ($+,-,\times ,÷$).

This is like applying detergent and softener separately on dirty clothes to get clean, soft clothes.

$f(x)$

$=$

$x+1$

$f(1)$

$=$

$1+1$

$=$

$2$

$g(x)$

$=$

$2x+4$

$g(1)$

$=$

$2(1)+4$

$=$

$6$

$\Downarrow$

$(\underline{f}+\underline{g})(1)$$=$$\underline{f(1)}+\underline{g(1)}$$=$

$2$

$+$

$6$

$=$

$8$

Alternatively, we can combine the two functions using the given operation ($+,-,\times ,÷$), and then plug the input into the combined function to determine the final output.

This is like using a pod that contains both detergent and softener to turn the dirty clothes into the clean, soft clothes.

$(\underline{f}+\underline{g})(x)$$=$$\underline{f(x)}+\underline{g(x)}$

$=$

$\underline{x+1}+\underline{2x+4}$

$=$

$3x+5$

$\Downarrow$

$(\underline{f}+\underline{g})(1)$

$=$

$3(1)+5$

$=$

$8$

Notice that both methods get us the same final results!