FUNCTIONS: In the space provided, type the answer in descending order as it applies without any spaces between the letters, numbers, or symbols.

Question

Type the composition  of the given functions:

f(x) = x² + 2x − 6 and g(x) = x + 5.

Answer 1

The function symbology f(x) means that you are about to write a "rule" called function "f" and that rule tells you what to do for the input "x". If it said f(a) it would tell you what to do with the input "a". If the function is g and the input is "f(x)" then the rule g would tell you what to do with the input "f(x)" You would write that as g(f(x)) [which also is shorten into ].

In this case g(x) tells you to add 5 to the input (the rule is g(x) = x + 5). Since f(x) = x² + 2x − 6 then we take that as the input and add 5 so g(f(x)) = [x² + 2x − 6] + 5 or (combining like-terms) x² + 2x − 1

So   = x² + 2x − 1