Question

f and g denote two motions. Is it true that f ◦ g is a translation...

f and g denote two motions.

Is it true that f ◦ g is a translation if and only if both f and g are translations? Justify your answer.

Homework Answers

Answer #1

False : If and   both are translation then is also an translation but if is an translation but    and   may not be an translation for example ,

is defined by .

   is defined by .

Then ,

So ,

That is is an translation but    and   is not an translation .

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
Define g(x) = f(x) + tan-1 (2x) on [−1, √3/2 ]. Suppose that both f'' and...
Define g(x) = f(x) + tan-1 (2x) on [−1, √3/2 ]. Suppose that both f'' and g'' are continuous for all x-values on [−1, √3/2 ]. Suppose that the only local extrema that f has on the interval [−1, √3/2 ] is a local minimum at x = 1/2 . (a) Determine the open intervals of increasing and decreasing for g on the interval [1/2 , √3/2] . (b) Suppose f(1/2) = 0 and f(√3/2) = 2. Find the absolute...
1. a True or False? If ∫ [ f ( x ) ⋅ g ( x...
1. a True or False? If ∫ [ f ( x ) ⋅ g ( x ) ] d x = [ ∫ f ( x ) d x ] ⋅ [ ∫ g ( x ) d x ]. Justify your answer. B. Find ∫ 0 π 4 sec 2 ⁡ θ tan 2 ⁡ θ + 1 d θ C. Show that ∫ 0 π 2 sin 2 ⁡ x d x = ∫ 0 π 2 cos...
Let f, g : X −→ C denote continuous functions from the open subset X of...
Let f, g : X −→ C denote continuous functions from the open subset X of C. Use the properties of limits given in section 16 to verify the following: (a) The sum f+g is a continuous function. (b) The product fg is a continuous function. (c) The quotient f/g is a continuous function, provided g(z) != 0 holds for all z ∈ X.
True or False...Provide your reasons If f(n) =o(g(n)), then f(n)=O(g(n)) If f(n) =O(g(n)), then f(n) ≤...
True or False...Provide your reasons If f(n) =o(g(n)), then f(n)=O(g(n)) If f(n) =O(g(n)), then f(n) ≤ g(n) 3.  If 1<a=O(na), then f(n)=O(nb) 4. A and B are two sorting algorithms. If A is O(n2) and B is O(n), then for an input of X integers, B can sort it faster than A.
Whether the products of two functions(f(x)+g(x)); f(x)g(x)) are odd or even if the two functions are...
Whether the products of two functions(f(x)+g(x)); f(x)g(x)) are odd or even if the two functions are both even or both odd, or if one function is odd and the other is even. Investigate algebraically, and verify numerically and using sepreadsheet.
Indicate whether the following statements are true or false and justify the answer. (I) If f...
Indicate whether the following statements are true or false and justify the answer. (I) If f and g are functions defined for all real numbers, and f is an even function, then f o g is also an even function. (II) If a function f, defined for all real numbers, satisfies the the equation f(0) = f(1), then f does not have an inverse function.
a) Suppose that we have two functions, f (x) and g (x), and that: f(2)=3, g(2)=7,...
a) Suppose that we have two functions, f (x) and g (x), and that: f(2)=3, g(2)=7, f′(2)=−4, g′(2)=6 Calculate the values of the following derivative when x is equal to 2: d ?x2 f (x)?|x=2 b) A spherical ice ball is melting, and its radius is decreasing at a rate of 0.8 millimeters per minute. At what rate is the volume of the ice cube decreasing when the radius of the sphere is equal to 12 millimeters? Give your answer...
the values of two functions, f and g, are given in a table. One, both, or...
the values of two functions, f and g, are given in a table. One, both, or neither of them may be exponential. Give the exponential models for those that are. HINT [See Example 1.] (If an answer does not exist, enter DNE.) x −2 −1 0 1 2 f(x) 0.18 0.9 4.5 22.5 112.5 g(x) 8 4 2 1 0.5 f(x) = g(x) =
If f is a differentiable function such that f′(x) = (x^2− 16)*g(x), where g(x)>0 for all...
If f is a differentiable function such that f′(x) = (x^2− 16)*g(x), where g(x)>0 for all x, at which value(s) of x does f have a local maximum? 1. At both x=-4,4 2. Only at x=-16 3. Only at x=4 4. At both x=-16,16 5. Only at x=-4 6. Only at x=16
Let m1 and m2 denote the true average ages (in years) of students at two different...
Let m1 and m2 denote the true average ages (in years) of students at two different colleges. Assume both population distributions are normal with equal variances. Calculate and interpret a 99% confidence interval for m1 - m2 using the following data. Sample Size Sample Mean Sample Standard Deviation College 1 10 25 2 College 2 9 24 3 Group of answer choices A) 99% C.I. is (-2.36, 4.36). The sample supports the claim that the two colleges` students have significantly...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT