Answer:
1 ≤ x < 1.75
Explanation:
You want the solution to f(4x -3) ≥ f(2 -x²), given the domain of f(x) is (-8, 4) and f is increasing on that domain.
Domain of x
The restriction on the domain of f(x) puts bounds on the values that x may have. In particular, we require ...
- -8 < 4x -3 < 4 ⇒ -5/4 < x < 7/4
- -8 < 2 -x² < 4 ⇒ |x| < √10
The first of these bounds is the most restrictive.
Inequality
The inequality can be rearranged to ...
x² +4x -5 ≥ 0
(x -1)(x +5) ≥ 0
x ≤ -5 or x ≥ 1 . . . . . values of x that make the product non-negative
Solution
The solution set is the overlap between the values of x that satisfy the inequality and the values of x that keep the arguments of f(x) within the domain of f. That overlap is the region ...
1 ≤ x < 7/4
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