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) .
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.
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) .
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.
To determine fx-gx, we need to subtract the second function gx from the first function fx:
fx = x^2 - 6x + 8
gx = x - 4
fx - gx = (x^2 - 6x + 8) - (x - 4)
To subtract the terms inside the parentheses, distribute the negative sign to each term in gx:
fx - gx = x^2 - 6x + 8 - x + 4
Next, combine like terms:
fx - gx = (x^2 -x) - (6x - 6) + (8 + 4)
fx - gx = x^2 - x - 6x + 6 + 12
Finally, simplify:
fx - gx = x^2 - 7x + 18
Therefore, fx - gx = x^2 - 7x + 18.