Suppose U = R. let p(x) : x 2 − 2x − 15 < 17, then the statement u : ∃p(x) is (true or false).

Q: Below is a table that describes the age (in years) and the sex of students at Whatsamata University.…

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Q: Define f (x) = 4+ x – x² and g(x) = 5x – 3. Define f(x) - - (f o g)(x) = (go f)(x). True False

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Q: Let f(x) = x³-212-9. If f(3) = 0, then (x-3) is a factor of f(x). O True O False

A: factor theorem states that if f(x) be a polynomial of degree n , and (x-a) is a factor of f(x) then…

Q: Let f(x) = x³ – 6x ln x + 6x + 1000. Find all x-coordinates of the inflection points. O x = -1 and x…

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Q: Which of the following is not a possible zero of f (x)=2x-5x+12?

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Q: Let A = {x € R : x < a} and B={x €R: x < b}, where a and b are real numbers. Show that sup(A+ B) =…

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Q: Let P(x) = ax² + bx³ + x +1 where a and b are real numbers. Find values of a and b such that P(2i) =…

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Q: C. Given f(x) = 3 – 2x – x2, Determine each of the following. a.) f(-6) b.) f c.) f(x²) d.) f(x – 1)

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Q: Let f(x) = 2x – 11 + 3(x + 2). Find all values of x for which f(x) is at most 0.

A: Solution: Consider the given function is: f(x) = 2x - 11 + 3(x+2) Simplifying the above we have f(x)…

Q: Find the Domain of 1, if f(=) 0(s-6) %3D O Domain: y is all real numbers O Domain: y N0 O Domain: NO…

A: Given f(x)=6(x-6)2 To find f-1, assume y=f(x) then swap variables to find f-1

Q: Suppose f(x) = 2x² + 6x + 2. Compute the following: A.) f( – 3) + f(1) = B.) f( – 3) – f(1) =

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Q: Let the domain of x be the set of negative real numbers. Then Vx, (1+ x² > 0) is a true statement a…

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Q: The domain of the function /1- a² – y² ln(a² + y2 – 1) is empty. True False

A: We have to check

Q: Suppose x ∈ R. Let p(x): x² - 2x - 15 < 17 then the statement x is (valid or invalid)?

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Q: Given f(x) = 3– 2x – x, Determine each of the following. C. a.) f(-6) b.) fG c.) f(r*) d.) f(x-1)…

A: Topic = Functions

Q: Show that x + 5[x²] is 0(x²).

A: This is a problem of complexity.

Q: Let F(a) be Z2. Show that a2 and a2+a are zeros of x3+x+1.

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Q: 1) Which set of values for x should be tested to determine the possible zeros of the function f (x)…

A: We need to find possible x values that needs to be checked where function is zero.   NOTE - As per…

Q: Find a → evaluation for the function (4n+1) 8¹ogn

A: Solution: f(n) = (4n + 1)8log n        = (4n + 1) (23)log n              [here , we assume base of…

Q: Let f(x) = x² + 7. Find and simplify: f(x + 6) - f(x) O 12x + 50 O 12x + 36 O 12x O 50 0 36 O 6x +…

A: We can simplify and find the correct answer in the below steps.

Q: Indicate if the function is bijective from R to R, f (x) = −3x + 4, justify your answer

A: Given f : R→R, f(x)=-3x+4 Here the function is linear function. f'(x)=-3&lt;0 for all x∈R Which…

Q: Find (fig) and indicate the domain of the quotient f(x)=x²-10x+116 and glx)=x²-5x-24.

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Q: Let f(x) = 2x – 5 and g(x) = x² – 7x + 2. Then (f o g)(x) = (go f)(x)

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Q: - Give the domain for k(a) in interval notation. x2 + 3x +2

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Q: Find In such that: F(x) = x²³-8x²+ 9x +18=0

A: The given polynomial fuction is

Q: (f – 9) (-3)

A: Givenf(x)=x3-6x2+11x-5g(x)=4x3-8x2-x+12

Q: Showthat fo= x| is Continuous evalyuhore- 1x1+1

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Q: If f(x) = 2x² - 8 and g(x) = 2x + 1, evaluate f(g(x)) when x = -3 -30 O-19 42 O46 60

A: Given: f(x)=2x2-8 and g(x)=2x+1

Q: Let x, y, and z be real numbers. Prove the following a. -(-x) = x b. (-x) * (y) = -(xy) and (-x) *…

A: I have provided detailed proof for each question in the Explanation section.Explanation:Let's go…