■ Prove that the function x) = { win = ²+ = = 0 x X 0, x f(x) satisfies the intermediate value property on R, but is not continu- ous at x = = 0.

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

A:

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: ) Is the function f(x) = differentiable on the open interval (-1,1)? x².

A:

Q: Let f be the function given by f(x) = Jax + b for x 2 where a and b are constants

A:

Q: Find x-intercepts of the function: x2 – 9 f (x) = Зх + 1 Select one: O a.x = 3 O b.x= -3, x= 3 C. X=…

A:

Q: determine the value of the parameter a that will make the function f(x) = [ax+1, x- -1

A: The given function is fx=ax+1,    x<-1x2-3,     x>-1 To find: Value of parameter 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: ,for x 1 Discuss the contuniuty of f andf'.

A:

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

A:

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 point at which the function is not analytic iz² – 2z ƒ(z) = 3z + 1 - i

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: