(c) Show that f(x)>0 for all values of x, x # -2.

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

A: Given that the function f(x) = x+3 +x-1 To find the domain of f(x).

Q: 9. Let f(x) = xr – 3x² + 3.

A:

Q: Evaluate f''(c) at the point. f(x) = (x2 - 4)(x3- 2), c = 1

A:

Q: Obtain the TSE of f(x) = 2x² in powers of (x-1)

A: To Find: The Taylor Series expansion of function 2x-2 with center x=1

Q: Find a formula for f-'(x) and (f -1)'(x) if f(x) = V х-2

A:

Q: 2 For f(x) x 5 and g(x)= 7- x, find b. the domain of f og (fo g)(x); а.

A: Consider the given functions.

Q: Let h(x)=f(x)g(x) where f(x)=2x2−4x, g(−2)=4, and g′(−2)=−5 what is h′(−2)?

A:

Q: Find and classify the extremes value of f(x)=6x* – 4x° over the interval [-2,2].

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Does the function f(x)=2^x approach a certain real number as the value of x increasing positively?…

A: f(x) = 2x clearly, 2x+1 = 27.2 > 2x  f(x+1) > f(x) or if a E R (i.e. a>0) then f(x+a) = 2x.…

Q: Find real values of x for which f(x) = 0. f(x) = x3 − x

A: Given: fx=x3-x To find the real values of x for which fx=0. Solution: Put fx=0 and then solve for x.…

Q: In the function:  f(x)= (5x)/((x^2)-25  How do you find the x-values of the inflection points?…

A: Given function is,

Q: Find (a) the domain of  f and (b) f-1 and its domain.   f(x)  = √ (3 -e2x)

A:

Q: Find R2,2(x) for f(x)

A: Given, fx=ln1+xx. We have to find R2,2x for fx. Here, R2,2x is called as Pade approximation. Pade…

Q: Show that the real-valued function f: R → R defined by f(x) = x° x E R. 3x2 + 3x + 1 increases for…

A: Answer

Q: Find and classify the extremes value of f(x) = 6x* – 4x° over the interval [-2, 2].

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find ao of the function f(x) = (n - x)2

A: The given function is: f(x)=14π-x2

Q: 7. Find the natural domain of the function f(x) = V4– 3x .

A:

Q: 22. Find the "natural" domain of the function f(x)=16r +Vx. x'-16x

A:

Q: f(x)=5sqrt(x+2) at x=7

A: Given: f(x)=5x+2f(x) has domain x≥-2

Q: 49. Find (f)'(3) if f(x) = x³ + x + 1.

A:

Q: 4. Given f(x) = v3 – e2, find the domain of f and f-1.

A:

Q: 3. For the function f (x) = 4x2 – 25, a) find f(-1) - %3D %3D b) find all x when f (x) = 0

A:

Q: Find the interval on which f(x)=x2-4x+3 is increasing and the interval on which it is decreasing

A: Answer

Q: Find f(x) =2x2+3x-5, then prove that f'(0) +3f'(-1)=0

A: Givenfx=2x2+3x−5To provef'0 +3f'−1=0

Q: Given the funci f(x + 1) = f(x) + f( – 3) = %3D - ||

A:

Q: (-2x² – 5x + 14,x 3 x= 3 continuous at x = 3. Justify the conclusion.

A: For given function f(x) ; -2x2 -  5x  + 14  , x < 3   .... (i) 19  , x = 3         ..... (ii)…

Q: Find ao of the function f(x)=(-x)², 0≤x≤ 2π

A:

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

A: Given:h(x)-f(x)g(x)f(x)=-3x2+2x-3g(x)=-3x2+4x+3

Q: Find f '(a) for f(x) = 3 − 2x + 4x2

A:

Q: Discuss the monotonicity of g (x), where g(x) = 2f + f(6-x) for all x e R. 2

A: Test for monotonicity:           let us consider a function is continuous on [a ,b] and it is…

Q: Calculate the derivative of the following functions

A:

Q: Given that f(x) = 7|x| + 3x  -1, Find: a) f(-x) b) -f(x) c) Is f(-x)= f(x)?

A:

Q: i) find f (x) given that f(x) = X-2 2x+1) k) Differentiate y= (2x+1 (x-x 1), get your answer in…

A:

Q: (42) For f(x) = -2r" + 5x° – 12x²5 + 10, the degree of f"(x) is

A:

Q: The domain of the function f(x, y) = In(-x² -+1) is: 4 x² + 4 x² + y? > 4 1 x² + y2 <4

A: See the attachment

Q: • The domain of f(x) 3-х is 1-x2 1. R 2. R/{1,-1} 3. R/{3} 4. (0, co)

A: Domain: The domain of the function is defined as the set of all input values for which the function…

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

A:

Q: 23) The domain of f(x) = Vx + 3 is

A: Consider the function

Q: If f(x)=2sin^-1(x^3), then f’(x)=?

A: Solution:

Q: The absolute Extrema of the function f(r) = -V-x² + 8x- 15 on its domain are .2

A:

Q: Find f'(-2) for f(x) x² +1

A:

Q: x=-2 of f(x)=√x²-1

A: Above question is solved.

Q: Find f' (x) for f (x) = 8x-3e. %3D

A:

Q: f(x) = x²+6x+5 2-1

A: I am attaching image so that you understand each and every step.

Q: Find the absolute extrema of f(x) = 2x³ – 21x² + 72x on the closed interval [0, 5].

A:

Q: 3 Let f(x) = 4.x² 5 and g(x)= 3.x + 7, find. -

A:

Q: Does f(x) = x3 - x - 5 have a real zero between 1 and 2?

A: Intermediate value theorem: Let f be a polynomial function. If f(a) and f(b) have opposite sign then…

Q: -3x Find f (x) given that f'(x)=x' +2-e* at (0,-1).

A: