(a) Show that the composition of two one-to-one functions,f and g, is one-to-one.(b) Express (f o g)-' in terms of f-' and g¬'.

Answered: Image /qna-images/answer/b7a3470d-02d9-4a2d-922e-a0efc5fe3c95.jpg

Answered: (a) Show that the composition of two…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

Exer. 27-32: (a) Use f' to prove that f has an inverse function. (b) Find the slope of the tangent line at the point P on the graph of f. 27 f(x) = x² + 3x³ + 2x-1; P(5, 1)
2. Consider the function f (x) = x¹ − 2x² + 3. (a) Find the intervals on which f is increasing / decreasing. (b) Find the intervals on which f is concave up/ concave down. Display your answer in table form, with a column for the intervals, columns for each factor, a column for the derivative, and a column for the function, as shown in lecture.
Let f(x) be a function with domain (-00, 2) U (2,00) and f'(x) = (5-x)(x+3)(x-7)² Determine all the x-values 2-2 where the local extrema occur. A. -3,5 B. -3,2,5 C. -3,2,5,7 D. -3,5,7 E. -3,7 A B Oc OD OE
A company's revenue from car sales, C (in thousands of dollars), is a function of advertising expenditure, a, in thousands of dollars, so C = f(a). (a) What does the company hope is true about the sign of f'? O The company hopes f'(a) is always positive. O The company hopes f'(a) is always negative. The company hopes f'(a) equals zero. The company has no sign preference. O The company hopes f'(a) is sometimes negative and sometimes positive. (b) What does the statement f'(100) = 2 mean in practical terms? O f'(100) means that if the advertising budget is $2,000, the company's revenue is $100. O f'(100) means that if the advertising budget is $100,000 the company's revenue is $2. O f'(100) means that if the advertising budget is $100,000 each extra dollar spent on advertising will bring in about $2 worth of sales. O f'(100) means that the company must sell 2 cars in order to pay for $100,000 worth of advertising. O f'(100) means that if the advertising budget is $2,000, each extra…
5. a) Identify f, f', and f' from the graph below. b) Sketch the graph of the derivative in the blank box. -4 c) State where the function is not differentiable and explain why.

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

(a) Show that the composition of two one-to-one functions, f and g, is one-to-one. (b) Express (f o g)~' in terms of ƒ-' and g='.