Question

Let f : [0,∞) → [0,∞) be defined by, f(x) := √ x for all x...

Let f : [0,∞) → [0,∞) be defined by, f(x) := √ x for all x ∈ [0,∞), g : [0,∞) → R be defined by, g(x) := √ x for all x ∈ [0,∞) and h : [0,∞) → [0,∞) be defined by h(x) := x 2 for each x ∈ [0,∞). For each of the following (i) state whether the function is defined - if it is then; (ii) state its domain; (iii) state its codomain; (iv) state the natural domain for the formula.

(a) f ◦ g

(b) g ◦ f

(c) h ◦ f

(d) f ◦ h.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let f ( x ) = cot ⁡ x for 0 < x < π ....
Let f ( x ) = cot ⁡ x for 0 < x < π . (a) State the range of f and graph it on the interval given above. (b) State the domain and range of g ( x ) = cot − 1 ⁡ x . Graph g ( x ) . (c) State whether the graph increases or decreases on its domain. (d) Find each of the following limits based on the graph of g ( x...
Let Let A = {a, e, g} and B = {c, d, e, f, g}. Let...
Let Let A = {a, e, g} and B = {c, d, e, f, g}. Let f : A → B and g : B → A be defined as follows: f = {(a, c), (e, e), (g, d)} g = {(c, a), (d, e), (e, e), (f, a), (g, g)} (a) Consider the composed function g ◦ f. (i) What is the domain of g ◦ f? What is its codomain? (ii) Find the function g ◦ f. (Find...
Let f : R → R be defined by f(x) = x^3 + 3x, for all...
Let f : R → R be defined by f(x) = x^3 + 3x, for all x. (i) Prove that if y > 0, then there is a solution x to the equation f(x) = y, for some x > 0. Conclude that f(R) = R. (ii) Prove that the function f : R → R is strictly monotone. (iii) By (i)–(ii), denote the inverse function (f ^−1)' : R → R. Explain why the derivative of the inverse function,...
a.)Consider the function f (x) = 3x/ x^2 +1 i) Evaluate f (x+1), and f (x)+1....
a.)Consider the function f (x) = 3x/ x^2 +1 i) Evaluate f (x+1), and f (x)+1. Explain the difference. Do the same for f (2x) and 2f (x). ii) Sketch y = f (x) on the interval [−2, 2]. iii) Solve the equations f (x) = 1.2 and f (x) = 2. In each case, if a solution does not exist, explain. iv) What is the domain of f (x)? b.)Let f (x) = √x −1 and g (x) =...
Show an example of F(x,y) defined on [0,+∞)× [0, +∞) such that (i) F(0,0) = 0,...
Show an example of F(x,y) defined on [0,+∞)× [0, +∞) such that (i) F(0,0) = 0, (ii) F(+∞,+∞)=1 (iii) for every x ≥ 0, F (x, y) is increasing in y; for every y ≥ 0, F (x, y) is increasing in x, (iv) and yet, F(x,y) is not a valid joint CDF function. That is, there is no random vector (X, Y ) whose joint CDF is F .
Let the function f and g be defined as f(x) = x/ x − 1 and...
Let the function f and g be defined as f(x) = x/ x − 1 and g(x) = 2 /x +1 . Compute the sum (f + g)(x) and the quotient (f/g)(x) in simplest form and describe their domains. (f + g )(x) = Domain of (f+g)(x): (f/g)(x) = Domain of (f/g)(x):
Let f: [0, 1] --> R be defined by f(x) := x. Show that f is...
Let f: [0, 1] --> R be defined by f(x) := x. Show that f is in Riemann integration interval [0, 1] and compute the integral from 0 to 1 of the function f using both the definition of the integral and Riemann (Darboux) sums.
Let f : R → R + be defined by the formula f(x) = 10^2−x ....
Let f : R → R + be defined by the formula f(x) = 10^2−x . Show that f is injective and surjective, and find the formula for f −1 (x). Suppose f : A → B and g : B → A. Prove that if f is injective and f ◦ g = iB, then g = f −1 .
1. In this problem, the domain of x is integers. For each of the statements, indicate...
1. In this problem, the domain of x is integers. For each of the statements, indicate whether it is TRUE or FALSE then write its negation and simplify it to the point that no ¬ symbol occurs in any of the statements (you may, however, use binary symbols such as ’̸=’ and <). i. ∀x(x+ 2 ≠ x+3) ii. ∃x(2x = 3x) iii. ∃x(x^2 = x) iv. ∀x(x^2 > 0) v. ∃x(x^2 > 0) 2. Let A = {7,11,15}, B...
Let⇀H=〈−y(2 +x), x, yz〉 (a) Show that ⇀∇·⇀H= 0. (b) Since⇀H is defined and its component...
Let⇀H=〈−y(2 +x), x, yz〉 (a) Show that ⇀∇·⇀H= 0. (b) Since⇀H is defined and its component functions have continuous partials on R3, one can prove that there exists a vector field ⇀F such that ⇀∇×⇀F=⇀H. Show that F = (1/3xz−1/4y^2z)ˆı+(1/2xyz+2/3yz)ˆ−(1/3x^2+2/3y^2+1/4xy^2)ˆk satisfies this property. (c) Let⇀G=〈xz, xyz,−y^2〉. Show that⇀∇×⇀G is also equal to⇀H. (d) Find a function f such that⇀G=⇀F+⇀∇f.