If f(x)=0.5x+3 then what is fofofof? (composite function)
f∘f∘f∘f
is the same as
f(f(f(x)))
Evaluate the innermost f(x) first, and the next, and the next, and then the outermost.
For example,
if f(x)=x^2+1;
then
f(f(x))=f(x^2+1)=[x^2+1]^2+1
f(f(x))=[(x^2+1)^2+1]^2+1
Post your answer for a check if you wish.
Sorry, I missed one of the f's:
f∘f∘f∘f
is the same as
f(f(f(f(x))))
3x+2
To find the composite function fofofof, we need to apply the function f repeatedly.
To begin, let's find fofof:
f(x) = 0.5x + 3
fof(x) = f(f(x))
Replacing the "x" in f(x) with f(x), we get:
fof(x) = 0.5(f(x)) + 3
Next, let's find fofof:
f(x) = 0.5x + 3
fofof(x) = f(fof(x))
Replacing the "x" in f(x) with fof(x), we get:
fofof(x) = 0.5(fof(x)) + 3
Finally, let's find fofofof:
f(x) = 0.5x + 3
fofofof(x) = f(fofof(x))
Replacing the "x" in f(x) with fofof(x), we get:
fofofof(x) = 0.5(fofof(x)) + 3
Now, to simplify this expression further, we need to substitute each subsequent "f" with the previous expression we found:
fofofof(x) = 0.5(0.5(0.5(fof(x)) + 3) + 3)
We can continue this process multiple times to find the value of fofofof for a particular value of x.