Problem 11
g(x) = x-1
g(-3) = -3-1 .... plug in x = -3
g(-3) = -4
Plug this into f(x)
Now compute f(-4)
f(x) = x^2
f(-4) = (-4)^2
f(-4) = 16
Answer: 16
=======================================================
Problem 12
f(x) and g(x) are two polynomials. When subtracting any two polynomials, we end up with some other polynomial. This idea is known as set closure. Set closure is where you take two items from one set, apply an operation to them, and the result is another item from the same set. Another example of this is adding two whole numbers. Adding two whole numbers leads to another whole number.
So in short, h(x) = g(x)-f(x) is a polynomial
The domain of any polynomial is the set of all real numbers. We can plug in any x value we want to get some output value for y.
Let's find the result of g(x)-f(x)
g(x) - f(x) = [ g(x) ] - [ f(x) ]
g(x) - f(x) = [ x^2-x+1 ] - [ 5x+3 ]
g(x) - f(x) = x^2-x+1 - 5x-3
g(x) - f(x) = x^2-6x-2
Domain: Set of all real numbers
