**Question:** Which of the following functions from ℝ to ℝ are invertible? - \( f(x) = \sqrt[3]{x} \) - \( f(x) = x^5 - 1 \) - \( f(x) = x^4 \) - \( f(x) = 2^x \) - \( f(x) = x^2 - 1 \) - \( f(x) = 2x + 7 \)

Q: Find the linearization of the function f(x) = √10 – x² at a = = 1 O L(x) = =¹²(x − 1) + 3

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Q: The function f is defined by f(x) = x-7. Find f (2y). f(2y) = ]

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Q: Let f(x) = 4x + 3. Determine (f ofo f)(x). (f o f o f)(x)

A: Composite functions: composite functions are the functions substituted inside the other function.…

Q: Suppose that f(z) = x² - y² - 2y + i(2x - 2xy), where z = x+iy. Write f(z) in terms of 2, and…

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Q: Consider the functions f(x) = x² 4 and g(x)=√x-2. Which of the following is an element of the domain…

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Q: Let f(x) = 2 + √√x − 6. Find ƒ−¹(x). ƒ−¹(x) Now for fun, verify that (ƒ o ƒ−¹)(x) = (ƒ−¹ ○ ƒ)(x) O =…

A: The given function fx=2+x-6. We have to find the inverse function f-1x.

Q: Let f(z) - 4z-1 pnd alz) - ar+b, where a pnd b are positive constants. If the composite

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Q: Find f′(x) and f′(c).

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Use the functions given by f(x) = 53√x - 1 O 1253√x - 1 53√√x + 1 O 1253√√x + 1 05√√x + 1 ○ 1 125 x…

A: given  f(x)=1125x-1given  g(x)=x3

Q: Find f(x) and g(x) such that h(x) = (fog)(x). 4 h(x) = (6x+3)* Choose the correct pair of functions.…

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Q: For function i, i(x+4)=3x+1. Find i(-1)

A: Given function is

Q: Let f(x) = 4+ (5x +9)³. Find f¹(x) = (1) · (√(x − 4) – 9) Find (ƒ(2)) -¹ = (¹) · (√(x-4) – 9)

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Q: Find h(0), h(x + 3), and h(-x) for h(x) = x + Vx² – 1. 2)

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Q: Consider the functions f (x) = 5x + 3 and g(x) = v8 – 2x. Find the domain of (gof)(x). %3D

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Q: The functions u and w are defined as follows. u (x) = -2x-1 w (x) = 2x²-2 Find the value of u (w…

A: u(w(3))=-33

Q: Find functions f and g so that fo g=H. H(x)=√x² +12 Choose the correct pair of functions. O A. f(x)…

A: We have given a composite function  f○g=H Hx=x2+12 Checking pairs (f○g)x=fgx Afx=x , gx=x2+12…

Q: 1 Let f(x) = x²-3x+2, g(x) = and h(x)=√1-x. Find f( - 6), g(-6), h(-6), h(a), and h(-x).

A: Let's evaluate the functions step by step. Given Functions 1.f(x)=x2−3x+2 2.g(x)=x​1​ 3.h(x)=1−x​…

Q: Given y = f(x), if f(2)= -3 f(4) = 5 f-¹(-7)=2 Decide if f(x) is invertible. Give a clear…

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Q: Let f(x) 1 and g(x) = 4x + 7. Then с — 3 - (f o g)(0) = (f o g)(x) =

A: Given:

Q: Find f-1 (x) for f(x) = 7x + 4. O 1-²=-²/x-1/ O f¹(x) = -7x+4 O---- O f-¹(x) = -7 x - 4

A: For finding the inverse of a function replace all x with y and all y with x and then solve for y.

Q: Let f(x) = 2x + 3 and g(x) = 5æ² + 4x Compute and simplify the following. (f + g)(x) =

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Q: 2. Determine fx(x); x² + 1 f (x) = 3x

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Q: 1 Let f(x) and g(x) = 4x + 5. - 4 | Then (f o g)(6) (f o g)(x) =

A: The solution is given below :