2) Let f(z) - Find f(2) and determine the domain for f and f1

Q: Let f(x) = V8 - x + 9. Determine f(x) and the the domain of %3D

A: Givenf(x)=8-x+9

Q: g(x, y) = In(2-x) 1-x2-y²

A: To find the domain of the function, g(x,y)=ln(2-x)1-x2-y2

Q: Determine the domain of the function f (x, y) In(3-y) 4- x2 – y2°

A: Given function is f(x,y)=ln(3-y)4-x2-y2 Domain is the set of values for which the function is real…

Q: Let F(x) = 2x^3 - 5x + 1 Explain, by using the Intermediate Value Theorem, why this function has (…

A: A polynomial function is everywhere continuous. A point x= a is said to be a x- intercept of a…

Q: Let f(x) = x2 - x - 4 and g(x) = 2x - 6, find g(f(-1)).

A: We have given; f(x) = x2 - x - 4 and g(x) = 2x - 6

Q: Let f(x) = x³ + 2, g(x) = x- - 3, and h(x) = 8x + 3. Find the rule for the function. %3D f-g

A: Given function is : fx=x3+2gx=x2-3hx=8x+3  To find the value of fx-gxhx

Q: he domain of the function f(x) = Vx+5 is In(3-x) %3D

A:

Q: Discuss the continuity of f(x) = 2x + 3 at x = −4.

A:

Q: Show that f(x)=x5-x3-1 has a zero between 1 and 2.

A:

Q: Let the function f be defined by -5x +4 for x 2 f (x) = { x2 +3 %3D - 1 Evaluate f(-1) + f(3)

A: fx=-5x+4for x<-1x2+3      for -1≤x≤21x≥2

Q: Consider the functions f(x) = x +7 and g(x) = 27 - x2. (a) Use algebra to find the x-values where…

A: f(x) = x+7g(x) = 27 -x2calculating intersect points :f(x) = g(x)

Q: 3. Consider a function f(2) that is analytic in a domain that includes the real axis. When z is…

A: Given that,                 fz is an analytic function in a domain that includes the real axis .  We…

Q: Let f(x) = V2 - x+ 8. Determine f-(x) and the the domain of f(z). f(x) = %3D Domain of f-(æ) =

A:

Q: Let f(x) = x2 - x - 4 and g(x) = 2x - 6.Find (g - f)(x).

A: Given

Q: 19. Show that f(x) = x² + 1 is not one-to-one, using values of f (not the horizontal line test).

A: To show: The function fx=x2+1 is not one to one. Concept used: The function is one to one is and…

Q: Let f(x) = V7 – x + 8. Determine f-(x) and the the domain of f -(x). f(x) = Domain of f-(æ) ||

A: Let us take y = f(x). So,               y=7-x+8Replace y by x.⇒x=7-y+8⇒y=-x2+16x-57 Thus, we get…

Q: True or False The domain of (f .g) (x) consists of thenumbers x that are in the domains of both f…

A: To determine the statementThe domain of f∘g(x) consists of the numbers x that are in the domain  of…

Q: Let f (x) = x²+1° 1) What is the domain of f ?

A: Consider the function  fx=xx2+1

Q: Find the constant a such that the function is continuous on the entire real line. 7sin x if x <0…

A: For a function to be continuous at x = a, it must satisfy the following condition:

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: Prove or disprove that f(x1x2) = f(x1)f(x2).

A: Consider the provided equation, fx1·x2=fx1fx2 Disproved the provided equation. First we let any…

Q: Use Intermediate Value Theorem and Bolzano's Theorem to show that f(x)=x^3 and g(x)=2x+3 intersect…

A: given functions are                                                     f(x)=x3g(x)=2x+3 if both the…

Q: Find the domain of the function 3 - x f(x) = In x + 5 %3D

A:

Q: Differentiate f  and find the domain of f .

A:

Q: Let f (x) = 2x and g (x) = 3x2 + 1, find(go f) (x). Show your work using the Equation Editor Tool.

A:

Q: Let f(x) = 6 + V2x + 11. Find ƒ ¯'(x). f- (x) = where the domain is [6, ∞)

A: The inverse function of a given function y=f(x) can be obtained by interchanging y and x in the…

Q: Use the Intermediate Value Theorem to show that f(x) = x2 + x − 2 has at least two zeros in the…

A:

Q: A function f is ________ on an interval when, for any x1 and x2 in the interval, x1 &lt; x2 implies…

A: To fill: The blank of the statement. Given: The statement is "A function f is ________ on an…

Q: Let flx)=-x²-x+6 and g(x)=2x+5 , find f(g\x))

A:

Q: Prove that f(x)=x^3+x-1 has a root in the interval [0,2]

A:

Q: Let f (2) = 1 Find all the points where f (2)is analytic. z + 3

A:

Q: Consider the function f defined by f(x) = (3 – x)(4 + 3x). What is f(-3)?

A: Given  f(x)=(3-x)(4+3x)

Q: what should n be if f(x) = Xn defineof a polynomial function?

A:

Q: 1. Let f (x) = 2x² – x – 1 and let g(x) = x – 1 Which statement is true?

A: Given, f(x)=2x2-x-1 and g(x)=x-1

Q: Let f(x) = x3 + 3, g(x) = x2 - 3, and h(x) = 3x + 3. Find the rule for the function. fgh

A: Use the rule of composite functions.

Q: Find and sketch the domain of the function. f(x, y) - In(4x2 - 4y²) y

A:

Q: Let f(x) = √20- x and g(x) = x² - x. Then the domain of fo g is equal to

A:

Q: (b) If f(x) = anx", specify the domain of f. %3D

A:

Q: Let f(x) = x2 - x - 4 and g(x) = 2x - 6, Find Find (g - f)(x).

A: the function given to us is f(x) = x2 - x - 4 and g(x) = 2x - 6  we have to find the value of (g -…

Q: Use the Intermediate Value Theorem to show that the function f(x) = 4x3 - 2x2 - 7 has a real zero in…

A: fx=4x3-2x2-7 Intermediate Value Theorem states that, if f is a continuous function on a, b and k is…

Q: 39. Let f(x) = 2x3 - 4. Find a function y = g(x) so that (f o g)(x) =x+2.

A: We use the definition of composition of functions to find y= g(x).

Q: Suppose k>0. What is the domain of F(x) =/k² – x² ?

A:

Q: Let f(x) = x + 10 and g(x) = x² – 9. Find the domain of (-) (x)

A: Solution of the problem as follows

Q: Let f(x) = x² + 2, g(x) = x-- 3, and h(x) = 8x + 3. Find the rule for the function. %3! %3D %3D f-g

A: Consider the given function as, fx=x3+2, gx=x2-3 and hx=8x+3

Q: Let f(x) = x3 + 2e*. %3D Show that f is one-to-one and confirm that f(0) = 2 |3| Find (f-1)'(x).

A: Solve the following

Q: 3. Find the domain of f(x) = 1- 1 X X

A: We have to find the domain of f(x)

Q: Find f such that f'(x) = x - 5 and f(0) = 3. f(x) = %3D

A: Given: f'x=x2-5 f0=3   Integrate the function with respect to x. ∫f'x=∫x2-5dxfx=∫x2dx-5∫1dx=x33-5x+C

Q: Use the Intermediate Value Theorem to show that f(x) = 2x3 − 3 has a zero in the interval [1, 2]

A: