Question

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Answer 1

1) a)

b) $g(x)=\left \{ g(x)\geq-2:\sqrt{x-2}-2 \right \}$

c) $h(x)=\frac{1}{x-1}-3$

2) a) The square root function has been reflected horizontally about the line y=0 and has formula $f(x)=-\sqrt{x}$ .

b) The square root function has been reflected vertically about the line x=0 and has formula $f(x)=\sqrt{-x}$ .

3) a) Given, f(x) = -2x²

Now, f(-x) = -2(-x²) = -2x² and -f(-x) = -[-2(-x)²] = 2x²

Since f(x) = f(-x), therefore the function is even.

b) Given f(x) = (1/x)+2x

Now, f(-x) = [1/(-x)]+2(-x) = -(1/x)-2x and -f(-x) = -[-(1/x)-2x] = (1/x)+2x

Since f(x) = -f(-x), therefore the function is odd.

c) Given f(x) = $\sqrt{x}$

Now, f(-x) = $\sqrt{-x}$ and -f(-x) = $-\sqrt{-x}$

Since neither f(x) $\neq$ f(-x) nor f(x) $\neq$ -f(-x), therefore the function is neither even nor odd.

4) a) f(x) = -8x-x³

Now, f(-x) = -8(-x)-(-x)³ = 8x+x³ and -f(-x) = -(8x+x³) = -8x-x³

Since -f(-x) = f(x), therefore the function is odd.

b) f(x) = (x+1)²

Now, f(-x) = (-x+1)² and -f(-x) = -(-x+1)²

Since neither f(x) $\neq$ f(-x) nor f(x) $\neq$ -f(-x), therefore the function is neither even nor odd.

c) f(x) = 7x⁶

Now, f(-x) = 7(-x)⁶ = 7x⁶ and -f(-x) = -7x⁶

Since f(x) = f(-x), therefore the function is even.

5) a) $f(x)=3\left(x+1\right)^3-2$

b) $g(x)=\left|x\right|+2$

6) a) $f(x)=\left \{ f(x)\leq2:\sqrt{x-1}+2 \right \}$

b) $g(x)=|x+1|-1$

7) a) $f(x)=-2(x+2)^2$

b) $g(x)=\left \{ g(x)\leq0:\sqrt{8-4x} \right \}$

8) a) $f(x)=\left \{ f(x)\geq-2:\sqrt{4(x-1)}-2 \right \}$

b) $g(x)=-2\left(x+2\right)^3-1$

9) a) $g(x)=-\frac{1}{5}\sqrt{x}$

b) $g(x)=-3x^{1/3}$

10) a) $g(x)=\frac{1}{2x-4}+3$

b) $g(x)=6\sqrt{x-6}-9$

11) a) $g(x)=4\sqrt{x+5}+2$

b) $g(x)=\frac{1}{2\left(x+1\right)^2}-9$

12) a) |x-11| = 3

b) |x-4| = 1/5

c) $|x-10|\geq17$

13) |x-80| = 0

14) $|p-0.11|\leq0.025$

15) $|x-81|\leq15$

16) $|x-4.7|\leq0.012$