Explanation Inverse of f is f − 1 . If f is a one-to-one function and g is the inverse of the function f . Then ( f ∘ g ) ( x ) = x for all x in the domain of g and ( g ∘ f ) ( x ) = x for all x in the domain of f . ( f ∘ g ) ( x ) = f ( g ( x ) ) = f ( f − 1 ( x ) ) = x And ( g ∘ f ) ( x ) = g ( f ( x ) ) = f − 1 ( f ( x ) ) = x For example: Let us take a function f ( x ) = 5 x + 4 and its inverse g ( x ) = x − 4 5 . Solve for ( f ∘ g ) ( x ) and ( g ∘ f ) ( x )

1st Edition

ISBN: 9780078035616

Author: Julie Miller

Publisher: MCG

See similar textbooks

Videos

Question

Chapter 4.1, Problem 7PE

To determine

To fill: The statement “Let f be a one-to-one function and let g be the inverse of f. Then (f∘g)(x)= _ and (g∘f)(x)= _”.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.1, Problem 6PE

Chapter 4.1, Problem 8PE

Students have asked these similar questions

1.2.19. Let and s be natural numbers. Let G be the simple graph with vertex set Vo... V„−1 such that v; ↔ v; if and only if |ji| Є (r,s). Prove that S has exactly k components, where k is the greatest common divisor of {n, r,s}.

Question 3 over a field K. In this question, MË(K) denotes the set of n × n matrices (a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is equivalent to A-¹? Justify your answer. (b) Let B be given by 8 B = 0 7 7 0 -7 7 Working over the field F2 with 2 elements, compute the rank of B as an element of M2(F2). (c) Let 1 C -1 1 [4] [6] and consider C as an element of M3(Q). Determine the minimal polynomial mc(x) and hence, or otherwise, show that C can not be diagonalised. [7] (d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write down all the eigenvalues. Show your working. [8]

R denotes the field of real numbers, Q denotes the field of rationals, and Fp denotes the field of p elements given by integers modulo p. You may refer to general results from lectures. Question 1 For each non-negative integer m, let R[x]m denote the vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m. x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent (a) Let vi = x, V2 = list in R[x] 3. (b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4) is a basis of R[x] 3. [8] [6] (c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a linear map. [6] (d) Write down the matrix for the map ƒ defined in (c) with respect to the basis (2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3. [5]

Chapter 4 Solutions

College Algebra Essentials

Ch. 4.1 - Skill Practice 1 Determine whether function f is a...Ch. 4.1 - Prob. 2SP Ch. 4.1 - Prob. 3SP Ch. 4.1 - Prob. 4SP Ch. 4.1 - Prob. 5SP Ch. 4.1 - Prob. 6SP Ch. 4.1 - Prob. 7SP Ch. 4.1 - Prob. 8SP Ch. 4.1 - Prob. 1PE Ch. 4.1 - Prob. 2PE

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The statement “Let f be a one-to-one function and let g be the inverse of f . Then ( f ∘ g ) ( x ) = _ and ( g ∘ f ) ( x ) = _ ”.

Videos

To fill: The statement “Let f be a one-to-one function and let g be the inverse of f. Then (f∘g)(x)= _ and (g∘f)(x)= _”.

Want to see the full answer?

Chapter 4 Solutions