Let g(x) x2 and f (x) x 2 for x R, and let h be the composite function h g f (a) Find the direct image h(E) of E x R 0 x 1 (b) Find the inverse image h1(G) of G x R 0 x 4

Question: Let g(x) := x2 and f (x) := x + 2 for x R, and let h be the composite function h := g

Let g(x) := x2 and f (x) := x + 2 for x ∈ R, and let h be the composite function h := g ο f.
(a) Find the direct image h(E) of E := {x ∈ R : 0 < x < 1}.
(b) Find the inverse image h1(G) of G := {x ∈ R : 0 < x < 4}.

Step by Step Solution

★★★★★

3.31 Rating (175 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a fE x 2 0 x 1 2 3 so hE gf... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

829-C-I (878).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Let f, g: R R, where g(x) = 1 - x + x2 and f(x) = ax + b. If (g o f)(x) = 9x2 - 9x + 3, determine a, b.

a. Let g(x) = 2x + 3 and h(x) = x 3 . Consider the composite function f(x) = g(h(x)). Find f -1 directly and then express it in terms of g -1 and h -1 . b. Let g(x) = x 2 + 1 and h(x) = x. Consider...

In this exercise we will establish the important formula: (a) Let G(t) := «10 [e-t2(x2+1)/(x2 + 1)]dx for t > 0. Since the integrand is dominated by 1/(x2 + 1) for t > 0, then G is continuous...

Let f (x) = Va + 4 and g (a) = x2 - 4. Use interval notation to determine the domain of the composite function and then find the composite function. (fog) (x) Domain: [-4,00) X Composite function: (f...

4. a. Suppose two groups in Grande Prairie sponsor river tours that include sightseeing and lunch. One charges a xed fee of $120 plus $8 per hour, and the other charges a xed fee of $100 plus $10 per...

Math 416-D13, Abstract Linear Algebra, Spring 2017 Homework 5, Due Friday, March 3, 2017 Read [FIS] Sections 2.3-2.5 Problems 1. Section 2.3 Problem 1 in [FIS]. 2. Section 2.3 Problem 2 in [FIS]. 3....

8. Let x1 = (1, 1, 0, 0), and x2 = (1, 0, 0, 1). Let V = L(x1, x2). (a) Let x = (1, 2, 1, 2). Find the projection p(x|V). (b) Find an orthonormal basis {z1, z2} for V using Gram-Schmidt algorithm....

Instruction: Need someone who can solve this. Please show your solution. Make sure the answer is right ma'am sir. Choose correct answers \fGiven: f(x) = 3x g(x) = x2 h(x) = x- 2 m(x) = Vx Find (h g)...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Math 1330 Precalculus Electronic Homework (EHW 2) Algebra Review You have 2 electronic homework assignments over Algebra Review (EHW 1 and EHW 2); be careful about choosing the correct EMCF title...

The following are unrelated transactions. 1. On March 1, 2011, Loma Corporation issued $300,000 of 8% non-convertible bonds at 104, which are due on February 28, 2028. In addition, each $1,000 bond...

Write a paper on Future Models for Workplace Structure in Technology

how do you get the standard costs using single plantwide rate

Which stage of the product life cycle is characterized by a rapid increase in sales? a. Introduction b. Growth c. Maturity d. Decline

Determine a region whose area is equal to the given limit. Do not evaluate the limit. ITT lim -tan-an

Let A be the area under the graph of an increasing continuous function f from a to b, and let Ln and Rn be the approximations to A with n subintervals using left and right endpoints, respectively....

(a) Express the area under the curve y = x5 from 0 to 2 as a limit. (b) Use a computer algebra system to find the sum in your expression from part (a). (c) Evaluate the limit in part (a).

Tammy Monahan is considering the purchase of a home entertainment center. The product attributes she plans to consider and the weights she gives to them are as follows Portability Sound projection...

How will the cash flow of franchises be impacted by AB 257 in the following categories (provided changes are proposed and implemented in these areas)? f. Mandatory insurance levels for employees...

Assuming the data in the following table for corporate bonds, compute the average hedge ratio (duration multiplier) at the average spread level for the three credit ratings (M1,M2, AND M3)