a. Determine whether f(x) = 5/(x+1) is a one-to-one function from R to R, if not, give a counter example. b. Determine whether h(x) = x3+2x2+1 is one-to-one function from R to R, if not, give a counter example.

Q: Let h(x) = f(x) – g(x). If f(x) = 5x² and g(x) = 2x³, what is h' (1)?

A:

Q: Given the function h (x) = -v2 – x, what is h (x)?

A:

Q: Let f(x) = { 2x-3. 3x²+2, if x < 3 if x ≥ 3 be a piecewise function. Evaluate Sof 0 f(x)dx=

A: We can find the integration of the piecewise function as below.

Q: Find the value of the following function at x = 3 and x = 4. Does the Intermediate Value Theorem…

A: Given: f(x)=-x3+3x2+2x+7. Substitute x=3 and x=4 in f(x). f(3)=-33+332+23+7=13&gt;0…

Q: do you agree with the contention that the functions f(x) = x+2 and g(x)=x2-4 /x-2 are the same in…

A: It is given that, f(x) = (x+2)     and     g(x) = ( x2-4)/(x-2) Then we will prove that f(x) and…

Q: Let h(x)=f(x)g(x) where f(x)=−4x^2−5x+1, g(1)=−5, and g′(1)=−4 what is h′(1)?

A:

Q: 1. Differentiate the following functions: a) f(x) = 43x²

A: We have to differentiate of the given function

Q: Given y = 4 for all real values of x, Can y be regarded as a function of x ? Give reasons.

A: Given y = 4 for all real values of x To determine whether y can be regarded as a function of x or…

Q: Evaluate the piecewise function at the given values of the independent variable. 4x +3 if x< 0 f(x)…

A: Given piecewise function is  fx=4x+3       if x&lt;03x+6       if x≥0

Q: What is the change of y with respect to x of the function s(x) = (3x¹ + 9x³)(x² - 6x +9) ? -9x²…

A:

Q: ) Find (f-g)(x) for the given functions. f(x)=3x²-x+5 and g(x) = 5x²-3

A:

Q: For the function f defined by f(x) = x2 - 4x + 1,

A: Given function: fx=x2-4x+1

Q: Consider the function f(t) = = -X 3-x (x − 3)² - if x 3

A:

Q: 1. Consider the function f(x) = -x² – 4x – 3 a) Determine f(-4), f(a), and f(a+ h).

A:

Q: 2 For the function f(x) = -x', find f'"(x), f'"(0), f'"(1), and f"(- 1).

A: To find the double derivative for the given function.

Q: For what value of c is the function f(x) = = C= C 7 2-4 (x+2)(x-3) x==2 x = 1 otherwise continuous…

A: Given :fx=c,      x=-27,        x=1x2-4x+2x-3   otherwise

Q: For the function f defined by f(x) = 2x*-8x²+10x²-7x+1 for x E R* Use the Ad-hoc Calculations method…

A: Big O notation is a mathematical notation that describes the limiting behavior of a function when…

Q: 1. Is the function f(x)= x³ + x−1 even, odd, or neither?

A:

Q: What is the value "L", if exists, when a variable "x" in f(x) approaches a certain number "d" in the…

A: Given: A function fx is given. To Find: What is the value "L", if exists, when a variable "x" in…

Q: f (x) = x³ - 3x²?+ 3x – 2 оn (— ох, о)

A:

Q: Find the most general function F such that F'(x) – 14. x5 || - F(x) = Σ

A:

Q: Let h(x)=f(x)+g(x). If f(x)=x4 and g(x)=6x3, what is h′(−3)?

A:

Q: Let h(x)=f(x)g(x). If f(x)=−2x2+2x+3 and g(x)=−x2−3x−4, what is h′(−1)?

A:

Q: Let h(x)=f(x)+g(x). If f(x)=6x and g(x)=3x^2, what is h′(−1)?

A:

Q: 3-Examine the existence of f'(a) of each function at the specified points: bf(e)= <2 bf(x) = 2x ,x22…

A: We have to find the existence of f'(a) for the functions 1. f(x)=4,   x&lt;22x, x≥2   at a=22.…

Q: If g is the function given by g(x) = 1/3 x^3 + 3/2x^2-70x+5 on which of the following intervals is g…

A:

Q: Let h(x)=f(x)g(x). If f(x)=x^2−1 and g(x)=−x^2−4x−2, what is h′(−2)?

A:

Q: If f is a function such that f(2) = 5 and f'(x) ≥ 3 for all x, what are the possible values of f(7)?

A: The given condition for the function is:

Q: Find a value for the constant k, if possible, that will make the function continuous. Skx², (2x + k,…

A: Answer: The solution is as given below:

Q: Consider the compound function:             (x - 2)3 for x less than or equal to 2 h(x) =  |x| for…

A:

Q: Given the functions defined by f(x) = 3x² – 2 and g(x) = x² – 2, calculate the following: (f •…

A: Ans:Given,fx=3x2-2 and gx=x2-2we have to find fog-2

Q: The domain for the function f(x) = V-2(x – 1) is

A:

Q: Let h(x)=f(x)+g(x). If f(x)=6x and g(x)=3x2, what is h′(−1)?

A: Add the given two functions and differentiate with respect to x

Q: 0.4x + 0.2, x 2 -

A: The given function f(x) is, f(x)=0.4x+0.2x&lt;21x=21.8x-2.6x&gt;2 A function is said to be continues…

Q: f(c) {}} [=+3 = < (3x + 1

A:

Q: Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x2 − 4/x − 2 are the…

A: I am not agreed with this fact that f(x) and  g(x) are the same in every respect. The reason behind…

Q: Evaluate the piecewise function at the given values of the independent 2x + 4 if x< 0 f(x) = 4x +6…

A:

Q: The function h(x)=1x+7h(x)=1x+7 can be expressed in the form f(g(x))f(g(x)) where…

A:

Q: Where is the function undefined and where is it equal to 0. f(x)=3e^2x-3

A: We can solve above question both through algebra and also through drawing it's graph. Both of them…

Q: Let h(x)=f(x)g(x). If f(x)=3x^2−x−4 and g(x)=−x^2+2, what is h′(−1)?

A:

Q: Let h(x)=f(x)g(x). If f(x)=2x2+1,g(1)=0, and g′(1)=−1, what is h′(1)?

A:

Q: Express the given function h(x) = 3√(x2 - 9) as a composition of two functions f and g so that h(x)…

A: Given function is  h(x)= x2-93.

Q: Evaluate the piecewise function at the given values of the independent variable. x2-4 if x#2 h(x) =…

A:

Q: Let h(x)=f(x)/g(x) where f(x)=x^2+5x−1, g(2)=−4, and g′(2)=−2 what is h′(2)?

A:

Q: For the function f(x)=3x", evaluale : f(Xth)=

A: F(x) = 3x2 , put x = x+h                                                            F(x+h) =3(x+h)2…

Q: For the function f(x) = (E)', find f-'(x). 8 Of (x) = (8/") || 4 Of (x) = (V8x)* f1 (x) = V (8æ)“…

A: Solution: The objective is to find the inverse of the given function

Q: Express the function h(x)=1x+8h(x)=1x+8 in the form f∘gf∘g. If g(x)=(x+8)g(x)=(x+8), find the…

A: The given function is h(x) = x + 8.We have to express it as a composition of two functions f(x) and…

Q: 2. Let f be the function defined by 9) f (x) = x²+2x+1 ,Find: -f (3) +fヒ3)

A:

Q: If we apply Rolle's Theorem to the function f(x) = 2x – 12x -7 on the interval [1, 5], how many…

A:

Q: Given the function f"(x) = -2x(x – 4)(x – 6), what conclusion can be drawn directly from the sign…

A: The given double derivative function is f"x=-2x3x-4x-6.