x+2 x<2 1) Let f(x)={ ax² – bx+3, ; 2

Q: Prove algebraic ally that any function of the form f(x)=ax2n+4 (where n is an integer) is symmetric…

A: The given function is fx=ax2x+4. To prove fx=ax2x+4 is symmetric to the y-axis, it is enough to…

Q: What values of a and b make the function f continuous everywhere? x² 4 a = f(x) = and b = - " X 2…

A:

Q: 6. Use algebra to determine whether the given functions are is even, odd or neither a) f(x) = -x³ +…

A: For a given function f(x)  If it satisfies the condition  f(-x) = f(x), then the function is Even.…

Q: 4х+7 (ii) If f(x)={ 1<x<2 determine whether the function f(x) is continuous 14x² -1 2<x<4 throughout…

A: Continuity of the function

Q: True or False.   If f(x) = a * x ^ 3 + b * x ^ 2 + cx + d where a 0, then f has at least one…

A: Given that: f(x)=ax3+bx2+cx+d, a≠0

Q: X + Y IF F 2+F(X)+F(Y) FOR ALL X, YeR 3 AND F(2).THEN DETERMINE F(X).

A:

Q: ) Find the values of the constant a so that the function f (x) will be continuous for all x. fax +…

A:

Q: F(x)=6-2x, 1<x<5

A:

Q: interval a sxsband a(n) function on a open interval a <x <b. Then there exists ace (a,b) such that…

A: It is problem of mean value theorem

Q: Let f be the function 6x-1 for x {/ Find the values of a and b that make the function continuous.…

A: we need to find values of a and b which make the given  function continuous.

Q: 2) Let f be a function given by (3x +2 if f(x) = { 3 (x² + 1_ if Find f(0), f(-2), ƒ(-1), ƒ(1) and…

A:

Q: Explain why f(x) satisfies the Intermediate Value Theorem.  f(x)=ex - x3 - 8  Use IVT to show that…

A: Given        f(x)=ex - x3 - 8  To prove that f(x) has a zero on [-2, 1]

Q: Let f(x) be a differentiable function on the interval [3,6]. If f(6) = 3 and 3 <f (x)<4 then which…

A:

Q: (4x+7 (ii) If f(x) = { 14x²-1 Isxs2 2<154 determine whether the function f(x) is continuous…

A: In this question we have to check whether the given function is continuous throughout its domain or…

Q: 12. Let f be the function f(x)={ x² - 3bx+2; x2 For what value of b is f continuous at x = 2 ? (A) 0…

A: To find For what values of b is f is continuous at x=2.

Q: x + Vx? -1 f (x) = X

A: Consider the given function, fx=x+x2-1x the domain of the function is the set of all possible real…

Q: Differentiate. y =x° In x- dy II

A:

Q: Q3) Test the continuity of the function f(x): -15x <0 0S X< 2 F(x) = 2х— 1 x+ 3 X = 2

A:

Q: What are intervals of concavity of the function f(x) = -2x + 6x² – 3 ? a. Concave upward on (-1, o0)…

A:

Q: Let f(x) = −3x² + 1 1 X3 + −xª. Find all local and absolute maxima and minima of f.

A:

Q: Write the formulas of fog for pairs of real functions f, g. (a) f(r) = x², 9(x) = x – 2 (b) f(x) =1,…

A: A composite function is generally a function that is written inside another function. Composition…

Q: Use Intermediate Value Theorem to check whether f(x) x- 2x -1 has at least one zero between x= -1…

A:

Q: Determine the type of functions from R to R with necessary figure. i) f(x) = 5x + 7 ii) f(x) = (x² +…

A: (i) fx=5x+7 This function is state line and has roots is x=-75

Q: Two functions f, g are defined as follows: Find a) ƒ-¹(2) b) (gof)(-4) f(x) = 3x + 5 g(x) = 2(1-x)

A:

Q: Let f (x) = 2x3 - 3x2 - 36x + 14. Also, let a = 0 and b = 1. (a) Show that the function f is…

A:

Q: b) Find the Constants "a" and "b" such that the following function is continuous for all real…

A: We have to properties of continuity first.

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.