1. Define h(x) = +y7x + 2, for all real numbers x > -. (a) Is h a one – to – one function? Why or why not? (b) If the co-domain is all real numbers greater than 0, is h an onto function? Why or why not?

Q: B) Test the functions continuity at the given poihts: (x²-x-6 1) f(x) 3D x * 3 ,at x 3, x 5 X-3 x =…

A: f(x)=x2-x-6x-3x≠35x=3

Q: 2. ASSUME f(x) IS CONTINUOUS AND DIFFERENTIABLE ON AN OPEN INTERVAL AS GRAPHED. WHICH OF THESE…

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: 2. Determine whether the function y= -x5 + x3 – 1 is even, odd, or neither. Justify your ans wer.

A:

Q: Which is the correct conclusion about the function h(x) ={V4- x2 if x - 3 if h has a removable…

A: Given function is: hx=-x-2    ;  if x<-24-x2     ;  if -2≤x<2x-3  ;  if x>2 We have to…

Q: | if x#3 6. %3D 15. Show that if the function g is defined by g(x) = if x=3 then g is not continuous…

A:

Q: Suppose f and g are real-valued functions defined on all of R, f is measurable, and g continuous. Is…

A: Given, that f and g are real valued function on ℝ and f is measurable and g is continuous function.…

Q: Suppose that ƒ : [a, b] → R is a continuous and one-to-one function. Prove that ƒ is strictly…

A:

Q: Show that f is not differentiable at x = 1 and has a corner in its graph there. x 1

A:

Q: Sketch the graph of the function g(x) = 3cos(2x) on the interval -2n s x s 2n.

A:

Q: Show that the function f : N → N, given by f(x) = 2x, is one-one but not onto.

A: If f(x1) ≠ f(x2) then we get:

Q: Find a function that is defined for all real numbers and has f'(x) that exists for all real numbers…

A:

Q: Prove that if (c, f(c)) is a point of inflection of the graph of f and f" exists in an open interval…

A: It is given that (c,f(c)) is a point of inflection of the function f.

Q: Determine the c which satisfy the conclusion of Rolle’s Theorem for the given function and interval.…

A:

Q: 19. Suppose f is a piecewise-defined function, equal to g(x) if x 2, where g and h are contin- uous…

A: Consider the given piecewise function. f=gx      x<2hx      x≥2 The functions g(x) and h(x) are…

Q: 1 Discuss the continuity of the function g(x) : on the interval [-1,2]. x2-4

A: Consider the given function and interval, f(x)=1x2-4 and [-1,2]   Now, check the value of the…

Q: and the domain of the function using interval notation. To enter ∞o, type infinity. To enter U, type…

A: We can solve this as follows:

Q: Suppose a function f is continuous on the interval [1, 5] except at x 3 and f(1) = 2 and A5) = 7.…

A: In this question we have to given two graphs one is holding IVT while another one is not

Q: Determine whether  the following statement is true or false, and explain why. A critical number c is…

A: Solution:GivenA critical number c is a number in the domain of a function ƒ for which ƒ′(c) = 0 or…

Q: Sketch the graph of a function that satisfies all of thegiven conditions.     f'(x)  and f"(x)  are…

A:

Q: 9. Consider the function f: R → R, defined by (x²sin(1/x) ifx # 0 f(x) = if x = 0 Then a. f is not…

A:

Q: Prove that f(a) = (z - 1)² + (x + 1) is an even function.

A: The given function,   f(x)=x-12+x+12

Q: Does there exist a function f such that f(0)  =-1, f(2)  =4, and f'(x) ≤ 2  for all  x?

A:

Q: Prove that if f(x) is a differentiable function everywhere and f'(x) # 1 for any value of x, then…

A: The objective here is to prove that the mentioned function f(x) has maximum one fixed point. Given:…

Q: Suppose that the function h is defined on the interval-2, 2) as follows. -2 if-2<x<-1 -1 if-1<x<0 h…

A: Given:     To determine: h(-2), h(-1.5), h(1)

Q: Let f (x, y) = 4-y² In(y–z²) %3D Draw a picture of the domain of this function.

A: x,y ∈R2

Q: Consider the function f with domain (-2, : 3|22 – 1| if – 2 < x < 1 2x2 + 2x – 4 f(x) = 3 if x = 1…

A:

Q: 7. Give an example of two functions h(x) and g(x), such that (h o g) (x) does not exist.

A: we need to find two functions h(x) and g(x), such that (hog)(x) does not exist. Let us take two…

Q: Suppose that ƒ(x) = x2 and g(x) = | x | . Then thecompositions( ƒ ∘ g)(x) = | x | 2 = x2 and (g ∘…

A: Given: The composite of the two functions are given as,

Q: 7. Show that the function f : R → R* defined by f(x) is not onto. x2 +1

A:

Q: Consider the function f with domain (-2, ∞): 3|22 – 1| if – 2 < x < 1 2x2 + 2х — 4 f(x) = 3 if x = 1…

A: Solution is given below:

Q: Use the intermediate value theorem to show that f(x) = e-x2− x has at least one root in the interval…

A:

Q: The function on ℤ defined by f(x)=-x^2-5 is onto. True or False ?

A: The given function is                  f(x) =x2-5   Graph:

Q: Define g(4) in a way that extends g(x) = (x2 - 16)/(x2 - 3x - 4) to be continuous at x = 4.

A: On simplification, we get

Q: Let h(x) = cos x and g(x) = x - l. Compute the composite functions h o g and g o h, and find their…

A:

Q: 2. Consider the function f with domain (-2, 0): 3|22 – 1| if – 2<r<1 2.r2 + 2x – 4 f(x) = 3 if r = 1…

A:

Q: Find c such that the function ² - 4 x c is continuous everywhere.

A:

Q: 5. Suppose that function f(x) satisfies f'(x) 0 at interval [a, b], then the graph of y = f(x) ( )…

A:

Q: (b) Suppose that f(x) = ൜βx2 − 3    if x ≤ 2βx + 2      if x &gt; 2 Find the value of β so that f(x)…

A: For continuity, left hand limit=right hand limit=f(x)

Q: 1. Suppose that f2(x) is a measurable function. Is it true that f(r) is measurable? Prove, or give a…

A:

Q: Let f(z) be a real valued function defined for satisfying f(1) = 1 and f'(2) = then lim f(z) =)…

A: Given function is, f'x=1x2+fx2 The above equation f'x is always positive which means fx  is always…

Q: If g (x) = 1 - x, defined at 0 ≤ x ≤ 1, graph its extension on the interval [-1, 1].

A: extension of the function

Q: If a function is real and continuous in the region from a to b and f(a) and f(b) and if both have…

A:

Q: Consider the function f with domain (-2, 0): 3|a2 – 1| if – 2 < x < 1 2x2 + 2x – 4 f(x) = 3 if x = 1…

A:

Q: (b) Suppose that f(x) =  βx2 − 3            if x ≤ 2 βx + 2             if x > 2 Find the value of β…

A:

Q: 1-What are Univalent Functions .

A: We define a function on complex numbers.

Q: 5.11. Prove that the function f(z) = Arg(z) is discontinuous at each %3D point on the nonpositive…

A: Solution

Q: Let f(x, y) = -e2"-y + In(3x – y). Find the domain of this function.

A:

Q: 1 Discuss the continuity of the function f(x) on the interval (0,2] and [-1,3] x2 -4

A: A function f(x) is said to be continuous in the closed interval [a,b] if→ f is continuous on (a,b).→…

Q: Define g(3) in a way that extends g(x) = (x2 - 9)/(x - 3) to be continuous at x = 3.

A: Here, the given function The function gx is continuous at  x=a, if the following holds: (i) ga is…