Let f(x) = x^2 + 7 and
g(x) = x-3/x
Find the composition
of (fºg)(-3)
Not necessarily looking for the answer but i don’t understand how to set up the question
replace the x in f(x) with g(x)
(x-3/x)^2 + 7 or did you mean ((x-3)/x)^2 + 7
Replace with 3
The first way would be the second way would be
-3 minus 3/-3 (-3-3)/-3 = -6/-3 or 2 squared = 4
-3-1 = -4 squared 4 + 7 = 11
16+ 7 = 23
(f º g) means that g(x) becomes the variable for f(x)
this is also written as ... f[g(x)] ... which might make it a little clearer
if ... f(x) = 2x + 1 ... and ... g(x) = 4x^2 ... then ... (f º g)(x) = 2(4x^2) + 1
To find the composition (fºg)(-3), we need to substitute the function g(x) into f(x), and then evaluate this composite function at x = -3.
1. Start by substituting g(x) into f(x).
f(g(x)) = f(x-3/x)
2. Now substitute -3 for x in the composite function.
f(g(-3)) = f(-3-3/(-3))
3. Simplify the expression within f().
f(-3-3/(-3)) = f(-3-(-1))
This simplifies to f(-2).
4. Evaluate f(-2) using the given function f(x).
f(-2) = (-2)^2 + 7
= 4 + 7
= 11
Therefore, the composition (fºg)(-3) is equal to 11.