Question

Use the following functions for questions 3 and 4.
fx= x2-6x+8 and gx=x-4
3. Determine fx-gx. 4. Determine f(x)g(x) .

Answer 1

Use the following functions for questions 3 and 4.
f(x)= x^2-6x+8 and g(x)=x-4
3. Determine f(x)-g(x). 4. Determine f(x)/g(x) .

Answer 2

To determine fx - gx, we subtract gx from fx:

fx - gx = (x^2 - 6x + 8) - (x - 4)

Simplifying this expression, we distribute the negative sign to each term in gx:

fx - gx = x^2 - 6x + 8 - x + 4

Combining like terms:

fx - gx = x^2 - 7x + 12

Therefore, fx - gx = x^2 - 7x + 12.

To determine f(x)g(x), we multiply fx by gx:

f(x)g(x) = (x^2 - 6x + 8)(x - 4)

To simplify this expression, we can use the distributive property:

f(x)g(x) = x^3 - 4x^2 - 6x^2 + 24x + 8x - 32

Combine like terms:

f(x)g(x) = x^3 - 10x^2 + 32x - 32

Therefore, f(x)g(x) = x^3 - 10x^2 + 32x - 32.

Answer 3

To determine f(x) - g(x), we subtract g(x) from f(x):

f(x) - g(x) = (x^2 - 6x + 8) - (x - 4)

Simplifying this expression, we distribute the negative sign to each term in g(x):

f(x) - g(x) = x^2 - 6x + 8 - x + 4

Combining like terms:

f(x) - g(x) = x^2 - 7x + 12

Therefore, f(x) - g(x) = x^2 - 7x + 12.

To determine f(x)/g(x), we divide f(x) by g(x):

f(x)/g(x) = (x^2 - 6x + 8) / (x - 4)

Since we cannot divide by zero, we need to check if x - 4 is equal to zero:

x - 4 = 0
x = 4

Therefore, x = 4 is not in the domain of f(x)/g(x).

So, f(x)/g(x) is undefined for x = 4.