Concept explainers
In Exercises 35—42, show that f and g are inverses of each other by verifying that
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
Precalculus: A Unit Circle Approach
- In Exercises 33–38, express the function, f, in simplified form. Assume that x can be any real number. 33. f(x) = V36(x + 2)² 34. f(x) = V81(x – 2)2 35. f(x) = V32(x + 2)³ 36. f(x) = V48(x – 2)³ 37. f(x) = V3x² – 6x + 3 38. f(x) = V5x2 – 10x + 5 %3Darrow_forwardLet f ( x ) = x 2 + 3 and g ( x ) = 3 x + 5. What isarrow_forward9) Let f(x) = (x + 2)² - 12. a) Sketch a "good enough graph" of f. b) Determine the number of solutions to the equation f(x) = -3 using the graph in in a). c) Work backward (applying inverse functions) to the equation f(x) = -3 for x. x =arrow_forward
- In Exercises 1-10, find f(g(x)) and g((x)) and determine whether each pair of functions f and g are inverses of each other. 1. f(x) = 4x and g(x) = 4 2. f(x) = 6x and g(x) = 7 x - 8 3. f(x) = 3x + 8 and g(x) 3 X - 9 4. f(x) = 4x + 9 and g(x) 4 x +5 5. f(x) = 5x – 9 and g(x) 9 x + 3 6. f(x) = 3x – 7 and g(x) 7. f(x) : 3 and g(x) 3 + 4 X - 4 2 8. f(x) 2 and g(x) = = + 5 X - 5 9. f(x) = -x and g(x) = -x 10. f(x) = Vx – 4 and g(x) = x + 4arrow_forwardLet f(x)=x2, g(x)=2x+5, and h(x)=x2-1 a. h[f(-2)] b. f[g(x-1)]arrow_forwardExercises 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_forward
- In Exercises 1-5, let f(x) = sin x, g(x) = x² + 1, and h(x) = 7x. Write a simplified expression for the composite function 1. f(g(x)) 2. f(g(h(x)) 3. (g o h)(x) 4. (ho g)(x) g(x) 5. f h(x)arrow_forwardLet f(x) = 8x2 - 5x and g(x) = 7x + 9.Find the composite.g[f(-3)]arrow_forwardEXERCISE 6 (PSAT – 20151028 Section 4, Q9) (Calculator permitted) f(x) = x + 4(x – 3) Which of the following is an equivalent form of the expression above that displays the zeros of the function as constants or coefficients in the expression? A) f(x) = x² + 4x – 12 B) f(x) = (x – 6)(x + 2) C) f(x) = (x + 6)(x – 2) D) f(x) = (x +2)² – 16arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning