Answer:
[tex](f\circ h)(2)=2[/tex]
Step-by-step explanation:
Composite Function
Given f(x) and h(x) real functions, the composite function named [tex](f\circ h)(x)[/tex] is defined as:
[tex](f\circ h)(x)=f(h(x))[/tex]
It can be found by substituting h into f.
We are given the functions:
[tex]f(x)=2x^2-9x+2[/tex]
[tex]h(x)=x^2-4[/tex]
It's required to find [tex](f\circ h)(2)[/tex]
As defined above:
[tex](f\circ h)(x)=f(h(x))[/tex]
Thus:
[tex](f\circ h)(2)=f(h(2))[/tex]
Find h(2):
[tex]h(2)=2^2-4=0[/tex]
h(2)=0
Now:
[tex](f\circ h)(2)=2(0)^2-9(0)+2[/tex]
[tex](f\circ h)(2)=2[/tex]
