Exercises 1—14, to establish a big-Orelationship, find witnessesCandksuch that
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Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
- Exercises 121–140: (Refer to Examples 12–14.) Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. 121. f(x) = 3 122. f(x) = -5 123. f(x) = 2x + 1 124. f(x) = -3x + 4 %3D 125. f(x) = 4x + 3 126. f(x) = 5x – 6 127. f(x) = -6x² - x + 4 128. f(x) = x² + 4x 129. f(x) = 1 – x² 130. f(x) = 3x² 131. f(x) = 132. /(x) 3D글 = = 132. f(: 133. f(x) = 3x² + 1 134. f(x) = x² –- 2 135. f(x) = -x² + 2r 136. f(x) = -4xr² + 1 137. f(x) = 2x - x +1 138. f(x) = x² + 3x - 2 139. f(x) = x' 140. f(x) = 1 – xarrow_forwardUse graphs to determine if each function f in Exercises 45–48 is continuous at the given point x = c. [2 – x, if x rational x², if x irrational, 45. f(x) c = 2 x² – 3, if x rational 46. f(x) = { 3x +1, if x irrational, c = 0 [2 – x, if x rational 47. f(x) = { x², if x irrational, c = 1 x² – 3, if x rational 3x +1, if x irrational, 48. f(x) : c = 4arrow_forwardIn Exercises 7–10, write a formula for ƒ ∘ g ∘ h. 7. ƒ(x) = x + 1, g(x) = 3x, h(x) = 4 - x 8. ƒ(x) = 3x + 4, g(x) = 2x - 1, h(x) = x2 9. ƒ(x) = sqrt(x + 1), g(x) = 1 /(x+4) , h(x) = 1 /x 10. ƒ(x) = x + 2 /(3 - x) , g(x) = x2 /(x2 + 1) , h(x) = sqrt(2 - x)arrow_forward
- In Exercises 15 – 28, a function f(x) is given.(a) Find the possible points of inflection of f.(b) Create a number line to determine the intervals onwhich f is concave up or concave down.16. f(x) = −x^2 − 5x + 7arrow_forwardIn Exercises 43–46, find the value(s) of x for which fxgx. f(x)=x2+2x+1,g(x)=5x+19arrow_forward(5.1,5.3) Let f(r) = Vx2 -4 and g(x) = 2r +2. Compute (gof)(x) and (fog)(z) and write down the domains of go f and fog in interval notation.arrow_forward
- a) Find the domain of f, g, f + g, f – & fg, ff, f/ g b) Find (f + g)(x), (f – g)(x), (fg)(x), (ff)(x), For each pair of functions in Exercises 17–32: 15. (8 and g/f. Find f+ g)(x), (f – g)(x), (fg)(x), (ff)(x), (f/8)(x), and (g/f)(x). 17. f(x) = 2x + 3, g(x) = 3 – 5x %3D 18. f(x) = -x + 1, g(x) = 4x – 2 19. f(x) = x – 3, g(x) = Vx + 4 20. f(x) = x + 2, g(x) = Vx – 1 21. f(x) = 2x – 1, g(x) = – 2x² 22. f(x) = x² – 1, g(x) = 2x + 5 23. f(x) = Vx – 3, g(x) : = Vx + 3arrow_forwardShow that exp(2²)| ≤ exp(2²) < for all = E C.arrow_forward9. Let f(x)=-x²–x+6 and g(x)=2x+5 , find f(g\x})arrow_forward
- Each of Exercises 25–36 gives a formula for a function y = f(x). In each case, find f-x) and identify the domain and range of f-. As a check, show that f(fx)) = f-"f(x)) = x. 25. f(x) = x 26. f(x) = x, x20 %3D %3D 27. f(x) = x + 1 28. f(x) = (1/2)x – 7/2 30. f(x) = 1/r, x * 0 %3D 29. f(x) = 1/x, x>0 x + 3 31. f(x) 32. f(x) = VE - 3 34. f(x) = (2x + 1)/5 2 33. f(x) = x - 2r, xs1 (Hint: Complete the square.) * + b x - 2' 35. f(x) = b>-2 and constant 36. f(x) = x? 2bx, b> 0 and constant, xsbarrow_forwardIf f(x) = 3x — 7, find the image of 2 and the preimage of 2arrow_forwardDescribe the long run behavior of f(t) = 5t° – 5t8 – 2t5 + 4 - - As t → 00, f(t) → ? v As t → 0, f(t) → ? varrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage