12.3: Exercises
- Page ID
- 49026
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Solve for \(x\).
- \(5x+6\leq 21\)
- \(3+4x> 10x\)
- \(2x+8\geq 6x+24\)
- \(9-3x< 2x-13\)
- \(-5 \leq 2x+5\leq 19\)
- \(15> 7-2x\geq 1\)
- \(3x+4 \leq 6x-2\leq 8x+5\)
- \(5x+2< 4x-18\leq 7x+11\)
- Answer
-
- \(x \leq 3\)
- \(\dfrac{1}{2}>x\)
- \(-4 \geq x\)
- \(x>\dfrac{22}{5}\)
- \(-5 \leq x \leq 7\)
- \(-4<x \leq 3\)
- \(x \geq 2\) (this then also implies \(x \geq-\dfrac{7}{2}\))
- no solution
Solve for \(x\).
- \(x^2-5x-14>0\)
- \(x^2-2x\geq 35\)
- \(x^2-4\leq 0\)
- \(x^2+3x-3<0\)
- \(2x^2+2x\leq 12\)
- \(3x^2<2x+1\)
- \(x^2-4x+4>0\)
- \(x^3-2x^2-5x+6\geq 0\)
- \(x^3+4x^2+3x+12 <0\)
- \(-x^3-4x<-4x^2\)
- \(x^4-10x^2+9\leq 0\)
- \(x^4-5x^3+5x^2+5x<6\)
- \(x^4-5x^3+6x^2>0\)
- \(x^5-6x^4+x^3+24x^2-20x\leq 0\)
- \(x^5-15x^4+85x^3-225x^2+274x-120\geq 0\)
- \(x^{11}-x^{10}+x-1\leq 0\)
- Answer
-
- \((-\infty,-2) \cup(7, \infty)\)
- \((-\infty,-5] \cup[7, \infty)\)
- \([-2,2]\)
- \(\left(\dfrac{-3-\sqrt{21}}{2}, \dfrac{-3+\sqrt{21}}{2}\right)\)
- \([-3,2]\)
- \(\left(-\dfrac{1}{3}, 1\right)\)
- \(\mathbb{R}-\{2\}\)
- \([-2,1] \cup[3, \infty)\)
- \((-\infty,-4)\)
- \((0,2) \cup(2, \infty)\)
- \([-3,-1] \cup[1,3]\)
- \((-1,1) \cup(2,3)\)
- \((-\infty, 0) \cup(0,2) \cup(3, \infty)\)
- \((-\infty,-2] \cup[0,1] \cup[2,5]\)
- \([1,2] \cup[3,4] \cup [5, \infty)\)
- \((-\infty, 1]\)
Find the domain of the functions below.
- \(f(x)=\sqrt{x^2-8x+15}\)
- \(f(x)=\sqrt{9x-x^3}\)
- \(f(x)=\sqrt{(x-1)(4-x)}\)
- \(f(x)=\sqrt{(x-2)(x-5)(x-6)}\)
- \(f(x)=\dfrac{5}{\sqrt{6-2x}}\)
- \(f(x)=\dfrac{1}{\sqrt{x^2-6x-7}}\)
- Answer
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- \(D=(-\infty, 3] \cup[5, \infty)\)
- \(D=(-\infty,-3] \cup[0,3]\)
- \(D=[1,4]\)
- \(D=[2,5] \cup[6, \infty)\)
- \(D=(-\infty, 3)\)
- \(D=(-\infty,-1) \cup(7, \infty)\)
Solve for \(x\).
- \(\dfrac{x-5}{2-x}>0\)
- \(\dfrac{4x-4}{x^2-4}\geq 0\)
- \(\dfrac{x-2}{x^2-4x-5}< 0\)
- \(\dfrac{x^2-9}{x^2-4}\geq 0\)
- \(\dfrac{x-3}{x+3}\leq 4\)
- \(\dfrac{1}{x+10}> 5\)
- \(\dfrac{2}{x-2}\leq \dfrac{5}{x+1}\)
- \(\dfrac{x^2}{x+4}\leq x\)
- Answer
-
- \((2,5)\)
- \((-2,1] \cup(2, \infty)\)
- \((-\infty,-1) \cup(2,5)\)
- \((-\infty,-3] \cup (-2,2) \cup[3, \infty)\)
- \((-\infty,-5] \cup(-3, \infty)\)
- \((-10,-9.8)\)
- \((-1,2) \cup [4, \infty)\)
- \((-\infty,-4) \cup[0, \infty)\)
Solve for \(x\).
- \(|2x+7|>9\)
- \(|6x+2|<3\)
- \(|5-3x|\geq 4\)
- \(|-x-7|\leq 5\)
- \(|1-8x|\geq 3\)
- \(1>\left|2+\dfrac{x}{5}\right|\)
- Answer
-
- \((-\infty,-8) \cup(1, \infty)\)
- \(\left(\dfrac{-5}{6}, \dfrac{1}{6}\right)\)
- \(\left(-\infty, \dfrac{1}{3}\right] \cup[3, \infty)\)
- \([-12,-2]\)
- \(\left(-\infty,-\dfrac{1}{4}\right] \cup\left[\dfrac{1}{2}, \infty\right)\)
- \((-15,-5)\)