Find constants a, b such that function f(x) given below is continuous on the entire Real line. (-x²+3x+le if x ≤a f(x) = ² - X²-5x-2 if a < x

Q: Find the domain of the function g(x) =√(x - 2)/(x - 5)

A: We can not have negative number inside the square root. x-2≥0 So, x≥2

Q: Show that f(x) = 2/x2 + 3x4 – 5x6 is an even function

A:

Q: Let f = x²-12x+27 x² - 6x +9 At which point f has a continuous extension?

A:

Q: 2 5 Let f (x) and g(x) = x+2° X-3

A:

Q: Find the domain (in interval notation) of the following functions

A: Domain: Domain of a function is the set of values of x for which the function is defined and real.

Q: A function f is defined by Ax + 5 f(x) 6x - 2 If f(1) = 4, find A.

A: Given: fx=Ax+56x-2  ……1   and, f1=4  ……2   To find: A

Q: Use the functions below to evaluate and simplify the function compositions. ƒ₁(x) = 4x² – 3x − 1,…

A: Given : f2(x)=7x2-3x-10   To Find : (f2ο f2)(-1)

Q: Find the domain of f if 2x + 1 f(x) = 2x2 – x – 1

A: Given: fx=2x+12x2-x-1 Domain of a function is set of all values of x for which function is defined…

Q: find the domain of f(x) x-12 / x(x2-16)

A: Numerator is a polynomial which is well defined for all real numbers. To find the domain we need to…

Q: Consider f(x) = (x - 1) / (x - 3). Use A = (-infinity, 3) union (3, infinity) as the domain. What is…

A: Let y = f(x). Then

Q: Give an example of a real function that is increasing on the interval (0,2), and decreasing on (2,…

A:

Q: Let x + 1 f(x) x + 6 ƒ−¹( − 2) = - =

A:

Q: Consider the function f defined by f(x) = (3 – x)(4 + 3x). What is f(-3)?

A: Given  f(x)=(3-x)(4+3x)

Q: Find the domain of f.  f(x) = x - 4/(x - 8)(x + 8)

A:

Q: Let f(x) = 9x + 7x2. Compute the difference quotient f(x+h)-f(x) h and simplify it so that it has…

A: The objective of this question is to compute the difference quotient of the function f(x) = 9x +…

Q: Prove that x -2x+2>0 for value of x.

A:

Q: Show that the function f(x) = 9 x8-5x³-3 is even, odd, or neither. f(-x) = f(x) is neither even nor…

A: Given: The given function is fx=9x8-5x3-3. To Prove: We have to show whether the given function is…