Question

Let f(x)=x−2 and g(x)=x2−3x+2 . Find g(x)f(x) and state the domain. Show your step-by-step work. (2 points)

Answer 1

To find the product of the functions g(x) and f(x), we simply multiply the two equations together.

We have:

f(x) = x - 2

g(x) = x^2 - 3x + 2

So, g(x)f(x) = (x^2 - 3x + 2)(x - 2)

Now, we distribute:

g(x)f(x) = x*(x^2 - 3x + 2) - 2*(x^2 - 3x + 2)

= x^3 - 3x^2 + 2x - 2x^2 + 6x - 4

Combine like terms:

g(x)f(x) = x^3 - 5x^2 + 8x - 4

As for the domain, we look at the restrictions on x. The function f(x) = x - 2 has no restrictions, it is defined for all real numbers. The function g(x) = x^2 - 3x + 2 is a polynomial, and polynomials are also defined for all real numbers. Therefore, the product g(x)f(x) = x^3 - 5x^2 + 8x - 4 is also defined for all real numbers.

So, the domain is all real numbers, or in interval notation, (-∞, ∞).