Problem Set 8

  1. Root Reflection in the y-Axis.

    h(x) = \sqrt{-x}

    *What is the domain of h(x)? * x\le0

    *What is the range of h(x)? * h(x)\ge0

  2. Combining Functions. a) 3x b) -x + 14 c) 2x2 + 7x - 49 d) \frac{(x+7)}{2x-7}
  3. Composition of Functions. a) x - 4 b) x - 1 c) (-\infty,\infty) d) (-\infty,\infty) e) 16x - 20
  4. Inverses. a) \frac{1}{2}(x+3) b) noinverse c) 3 \sqrt{\frac{(x+1)}{3}} d) 3 \sqrt{x} + 3
  5. Salary 1. a) 40000 b) x-400000 c) 0.03x
  6. Salary 2. d) g \circ f e) 0.03x-12000
  7. Salary 3. f) b + C g) 0.03x + 28000 h) 50650
  8. Salary 4. a) B b) \frac{100}{3}(x - 28000) c) 1100000
  9. Function of a Function.

    f(x)= 5x - 2

    g(x)= \frac{1}{5}(x+2)

    (f \circ g)(x) = x = (g \circ f)(x)

  10. Different Order, Different Result. \frac{4}{x} ; 4x ; \frac{1}{x} ; \frac{16}{x}
  11. Different Orders, Result is x. x^2 ; \sqrt{x} ; inverses
  12. Reflecting in the x-Axis. Multiply the function by -1.
  13. Shifting Polynomials.

    g(x)=x^6 - 1: 0 1 0 0

    h(x)=(x+3)^6 - 1: 0 1 0 3

  14. Shifting Rational Functions.

    f(x) = \frac{3}{x^3} + 2 : 2 0 0 0

    f(x) = \frac{3}{(x+1)^3} + 2 : 2 0 1 0

  15. Combining Functions. a) 20 b) 16 c) 148.373 d) 13.828