8. Given the following function f, define f(1) so that f is con- tinuous at x = 1, if possible: Зх — 1, ifx < 1 |x² + 1, if x > 1. f(x) =

Q: 3)Verify Rolle's Theorem for the function f (x) = 2x² + 3 defined over the interval -5, 5]. Justify…

A:

Q: Let f(x)=xsinx+V1-x Evaluate f'(-). Select one: а. 2 b. 0 C. d. 3

A: According to product rule of differentiation and according to power rule of differentiation .

Q: Is there a real function f(x) that is differentiable only at a point x?

A:

Q: Given the function fA(x) = x², g(x) = 3x – 4, find the composite function gof (where gof'means…

A: I have find inverse of f the composition

Q: 4. Let the function f: R - {2} → R be defined by f(x) x-5 2x - 3 Prove that ran(f) = R-{}}.

A: The given problem is to prove that the range of given function is Ran(f)=R-{1/2} . Given function…

Q: Determine whether each of the following is a function: (a) f : Z12 → Z6 by f([x]12) = [æ]6. (b) f :…

A: a

Q: 3. Find the domain of the following functions: a.) f(x) = V1-x Inx b.) f(x) = Vx - 1lr

A: solutionsince the given (3)(c)f(x)=1-xlnx(b) f(x)=x-l ln(x)use have to find the domain of the…

Q: A parallelogram is formed by the vectors [1, 2] and [3, -4]. Find the area of the parallelogram. O…

A: Given query is to find the area of parallelogram.

Q: Determine which of the points in the following list lie in the domain of the function f(x, y) =…

A: Let's find.

Q: Consider the following piecewise-defined function: f(x) = { 4-ax² if x ≤1 b 2x if x > 1 Find the…

A: Ans :Now we need to sketch the graph in the interval [-3,3]Firstly let's find some points on the…

Q: Evaluate (f x g)(2), given that f(z) - and g(z) -. 2. de".

A:

Q: Let f(x) = 1+ V7x +1. Determine the largest possible domain of f(x) Select one: • [-1/7, +o0)

A: Given function is  fx=1+7x+1

Q: ,for x 1 Discuss the contuniuty of f andf'.

A:

Q: The function x2 f(x) = 1 - x is decreasing on (0, 1). Select one: O True O False

A:

Q: 3)Verify Rolle's Theorem for the function f(x) = 5² + 3 defined over the interval [-4, 4]. Justify…

A:

Q: Let f be a function defined on [11, 25]. Suppose for every x = (11, 25) d. dx -f(x) = 0. If f(12) =…

A: Given query is to find the value o f(24).

Q: A function f has the form f(x) = Aekx. Find f if it is known that f(0) = 140 and f(1) = 266. (Hint:…

A:

Q: On what domain is the function f(x) = 4x2 – 5x – 6 continuous? |

A: