|
Question 1134048: (8 pts) Let f(x) = (x + 7)/(x- 5)^2
Calculate f(-3). Show the answer in exact form, simplified
State the domain of the function.
Determine f(a+3) and simplify as much as possible. Show work.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f(x) = (x + 7) * (x - 5)^2
f(-3) = (-3 + 7) * (-3 - 5)^2
simplify to get f(-3) = 4 * (-8)^2
simplify further to get f(-3) = 4 * 64
simplify further to get f(-3) = 256
that's your solution to the first part.
for the second part, start again with f(x) = (x + 7) * (x - 5)^2
replace x with a + 3 to get:
f(a + 3) = (a + 3 + 7) * (a + 3 - 5)^2
combine like terms to get:
f(a + 3) = (a + 10) * (a - 2)^2
since (a - 2)^2 is equal to a^2 - 4a + 4, the equation becomes:
f(a + 3) = (a + 10) * (a^2 - 4a + 4)
simplify to get:
f(a + 3) = a * (a^2 - 4a + 4) + 10 * (a^2 - 4a + 4)
simplify further to get:
f(a + 3) = a^3 - 4a^2 + 4a + 10a^2 - 40a + 40
combine like terms to get:
f(a + 3) = a^3 + 6a^2 - 36a + 40
that's your final equation for f(a + 3).
to see if the final equation is equivalent to the starting equation, select a random value for a and then evaluate the starting equation and the final equation to see if they provide the same answer.
your starting equation was f(a + 3) = (a + 3 + 7) * (a + 3 - 5)^2
your final equation was f(a + 3) = a^3 + 6a^2 - 36a + 40
let a = 5.
your starting equation becomes f(5 + 3) = (5 + 3 + 7) * (5 + 3 - 5)^2
this becomes f(8) = 15 * 9 = 135
your final equation becomes f(5 + 3) = 5^3 + 6*5^2 - 36*5 + 40
this becomes f(8) = 125 + 150 - 180 + 40
this becomes f(8) = 135
starting equation and final equation provide the same answer, so the simplification must have been good.
|
|
|
| |
