Technical Mathematics, Sixth Edition

4.3. CHAPTER 4 REVIEW PROBLEMS

1. Which of the following relations are also functions?

   1. y = 5x³ − 2x² Is a function

   2. x² + y² = 25 Not a function

   3. Not a function

2. Write y as a function of x if y is equal to half the cube of x, diminished by twice x. y = x³/2 − 2x

3. Write an equation to express the surface area S of a sphere as a function of its radius r. S = 4πr²

4. Find the domain and range for each function.

   1. 

   2. 

5. Label each function as implicit or explicit. If it is explicit, name the dependent and independent variables.

   1. w = 3y − 7 Explicit; y independent, w dependent

   2. x − 2y = 8 Implicit

6. Given y = 3x − 5, write x = f(y). x = (y + 5)/3

7. Given x² + y² + 2w = 3, write w = f(x, y). w = (3 − x² − y²)/2

8. Write the inverse of the function y = 9x − 5. y = (x + 5)/9

9. If y = 3x² + 2z and z = 2x², write y = f(x). 7x²

10. If f(x) = 5x² − 7x + 2, find f(3). 26

11. If f(x) = 9 − 3x, find 2f(3) + 3f(1) − 4f(2). 6

12. If f = 7x + 5 and g(x) = x², find 3f(2) − 5g(3). 12

13. If f(x, y, z) = x² + 3xy + z³, find f(3, 2, 1). 28

14. f(x) = 8x + 3 and g(u) = u² − 4, write f[g(u)]. 8u² − 29

15. If f(x) = 5x, g(x) = 1, and h(x) = x³, find

    

16. Is the relation x² + 3xy + y²