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

Explanation:

Given that there are two functions f and g as

`f(x) = √(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) = √(4x+9)`

b)
`gof = g{f(x)} = g(√(x) )=4√(x) +9`

c)
`fof = f(√(x) ) = \sqrt[4]{x}`

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