Let f(x)=x^2+1 and g(x) = x-2. What is f०g(-2)?
First, we need to find g(-2):
g(-2) = -2 - 2 = -4
Now, we can find f(g(-2)):
f(g(-2)) = f(-4) = (-4)^2 + 1 = 16 + 1 = 17
Therefore, f०g(-2) = 17.
what is the process
Sure! The process involves first finding g(-2) by substituting x=-2 into the expression for g(x):
g(-2) = -2 - 2 = -4
Next, we use the result of g(-2) and substitute it into f(x) to find f(g(-2)):
f(g(-2)) = f(-4) = (-4)^2 + 1 = 16 + 1 = 17
So, the final answer is 17. This process is known as the composition of functions, where you first find the value of the inner function (g(x) in this case) and then substitute that result into the outer function (f(x)).