Final Answer:
The value of (8-f)(x) is 13x-43. Option A is answer.
Step-by-step explanation:
To find (8-f)(x), we can substitute f(x) into the expression 8-f(x).
f(x) = x-2x-5
Substituting f(x) into the expression, we get:
8-f(x) = 8-(x-2/x-5)
Expanding the parentheses, we get:
8-f(x) = 8-x+2/x-5
Combining like terms, we get:
8-f(x) = 13-7x/x-5
Multiplying both sides of the equation by x-5, we get:
(8-f(x))(x-5) = 13x-7x
Expanding the left side of the equation, we get:
8x-40-f(x)x+5f(x) = 13x-7x
Combining like terms, we get:
-35-f(x)x+5f(x) = 6x
Factoring out f(x), we get:
f(x)(-x+5) = -35+6x
Substituting f(x) = x-2/x-5 into the equation, we get:
(x-2/x-5)(-x+5) = -35+6x
Expanding the left side of the equation, we get:
-x^2+5x-2x+10/x-5 = -35+6x
Combining like terms, we get:
-x^2+3x+10/x-5 = -35+6x
Multiplying both sides of the equation by x-5, we get:
(-x^2+3x+10)(x-5) = -35x+30x-175
Expanding the left side of the equation, we get:
-x^3+8x^2-25x+50 = -5x-175
Combining like terms, we get:
-x^3+8x^2-30x+50 = -175
Rearranging the terms, we get:
x^3-8x^2+30x-175 = 0
This is the cubic equation that represents the expression (8-f)(x).
Option A is answer.