Question

For f left parenthesis x right parenthesis equals StartRoot x EndRoot and g left parenthesis x right parenthesis equals 4 x plus 9 comma find the following composite functions and state the domain of each. ​(a) fcircleg ​ (b) gcirclef ​ (c) fcirclef ​ (d) gcircleg

Answer 1

Answer:

Step-by-step explanation:

Given that there are two functions f and g as

$f(x) = \sqrt{x} \\g(x) =4x+9$

We have to find the composition of functions.

Composition functions are calculated as the first function inside bracket and then the outside function of answer inside.

a)$fog= f{g(x)} =f(4x+9) = \sqrt{4x+9}$

b) $gof = g{f(x)} = g(\sqrt{x} )=4\sqrt{x} +9$

c) $fof = f(\sqrt{x} ) = \sqrt[4]{x}$

d) $gog = g(4x+9) = 4(4x+9)+9\\= 16x+45$