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Mark53
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Homework Statement
Let f(x) = 1−3x−2x^2 , x ∈ [−2, −1]. Use the Horizontal Line Test to show that f is 1–1 (on its given domain), and find the range R of f. Then find an expression for the inverse function f −1 : R → [−2, −1].
The Attempt at a Solution
I have already done the horizontal line test but I am unsure about my working out for the other parts below
would the range just be:
f(-2)=-1
f(-1)=2
y ∈ [−1, 2]
finding expression for inverse function
1−3x−2x^2=y
-2x^2-3x-y+1=0
using quadratic formula
x=(3-sqrt(-8y+17)/4 as (3+sqrt(-8y+17)/4 lies outside the range
Is this correct?