Answer:
(f*g)(0)=-2
f(g(0))=5 I think you meant this one based on your answer. Please read lower half of explanation for this answer. Please ask me any question on this that you have.
Step-by-step explanation:
(f*g)(0) means f(0)*g(0).
f(0) means to replace x with 0 in x^2+1 (since g(x)=x^2+1).
g(0) means to replace x with 0 in x-1 (since g(x)=x-2).
f(0)=0^2+1=0+1=1
g(0)=0-2=-2
So (f*g)(0)=f(0)g(0)=(1)(-2)=-2.
But I guess you didn't mean this because you said the answer is 5...
Oh maybe you mean
[tex](f \circ g)(0)[/tex]?
[tex](f \circ g)(0)[/tex] means [tex]f(g(0))[/tex].
So f(g(0))...we start with the inside first... that is g(0)?
g(0)=-2 (we found this above)
f(g(0))
f(-2) ->I replaced g(0) with -2
Now f(-2) means to replace x with (-2) in x^2+1 (since f(x)=x^2+1)
So let's do that:
(-2)^2+1
4+1
5
