Let R be the ring of all functions from R to R. Let I be the subset consisting of those functions f such that f(2)=0. Then prove that I is a subring of R. Moreover, show that it is an ideal of R.

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A: Given:  NT=21T2-80T+24 , 4<T<34 Tt=6t+1.8T

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A: The given integral is sec2(4x).

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Q: What's the answer?

A: Since you have posted multiple question, we will solve only first question for you. To get remaining…

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A: The given function fx=5x. (a) Obtain the function fx=5x shifting 2 units upward as shown below. In…

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Q: Noah says, "I worked the problem from left to right and ended up with `20-45x`."

A: NO, I don't agree with Noah. His approach is incorrect.

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Q: Evaluate the expressions using the order of operations. (- 14 + 18) - 2+ (12- 16) (- 14 + 18)? - 2+…

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A: A). a=$3000,  r=3%=0.03  &  k=4.   B). Put a=$3000,  r=0.03,  k=4 & t=7 in At=a1+rkkt, we…

Q: How do you tell if a solution is an extraneous solution?

A: Solve the given problem.

Q: How do I solve #4-6?

A: Solution :-

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A: 1) f(g(3))  Since ,  g(3)= 5 So,.     f(g(3))=f(5) = 1 2),  g(f(1))  Since.   f(1) = 3 Then ,…

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A: The functions f(x) and g(x) are piece-wise functions. Comparing both the graphs the function f(x)…

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Q: could you solve the second question as well

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A: Consider the given graph: Observe the following: Maximum input is 2. Minimum input is -3. Maximum…

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A: To find the composition values , 1)fg32)gf03)ff24)gg5 For finding this values from the graph we have…

Q: The second question wasn't answered.

A: Probability is the measure of the chance that an event is likely to happen. It is calculated by…

Q: How do you find lcd.

A: The Least common denominator or lowest common denominator (LCD) for a set of fractions that you want…

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A: It is know that, If c denotes the length of the hypotenuse and a and b denote the lengths of the…

Q: How do I evaluate the following 2 equations

A: Given f(x)=x2+9, g(x)=-4x+2 f(g(x))=f(-4x+2)=(-4x+2)2+9=16x2+4-16x+9 =16x2-16x+13 (f-g)(x)=…

Q: how did you get 2x in part c?

A: Joint probability density is used to understand the probability value of several continous random…

Q: how do you use math in real life?

A: Use of mathematics in real life

Q: Can you write this all out? So I can understand the steps clearly.

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Q: How do I use R

A: R  is a programming software  and free software environment for statistical computing  and graphics…