Answer:
Part 1) [tex]f(g(x))=3(x^2)+2[/tex]
Part 2) [tex]g(f(5))=289[/tex]
Step-by-step explanation:
we know that
A composite function is a function that depends on another function. A composite function is created when one function is substituted into another function
we have
[tex]f(x)=3x+2[/tex]
[tex]g(x)=x^{2}[/tex]
Part 1) Determine f(g(x))
To find f(g(x)) substitute the function g(x) as the variable in function f(x)
so
[tex]f(g(x))=3(x^2)+2[/tex]
Part 2) Determine g(f(x))
To find g(f(x)) substitute the function f(x) as the variable in function g(x)
so
[tex]g(f(x))=(3x+2)^2[/tex]
For x=5
[tex]g(f(5))=(3(5)+2)^2[/tex]
[tex]g(f(5))=289[/tex]
