Answer:
B
Step-by-step explanation:
So we have the two functions:
[tex]f(x)=-2x^2-5x+1\text{ and } h(x)=3(x+3)^2-11[/tex]
And we want to find:
[tex]h(f(-1))[/tex]
So, find f(-1) first. Substitute -1 into f(x):
[tex]f(-1)=-2(-1)^2-5(-1)+1[/tex]
Square:
[tex]f(-1)=-2(1)-5(-1)+1[/tex]
Multiply:
[tex]f(-1)=-2+5+1[/tex]
Add:
[tex]f(-1)=4[/tex]
Now, substitute this into h(f(-1)):
[tex]h(f(-1))=h(4)[/tex]
So, substitute 4 into h(x):
[tex]h(4)=3(4+3)^2-11[/tex]
Add:
[tex]h(4)=3(7)^2-11[/tex]
Square:
[tex]h(4)=3(49)-11[/tex]
Multiply:
[tex]h(4)=147-11[/tex]
Subtract:
[tex]h(4)=136[/tex]
So, our answer is B.
And we're done!
