x+1, x<0 f(x) = 0, x=0 (x² + 1, x>0 Can also be displayed as: ) = [ x+1 when x < 0, 0 when x Is f(x) continuous at x = 0? Why or why not? = 0, x²+1 when x > 0]

Q: Let f and g be functions of x, where a is an unknown constant. What is a valid expression for (-)'…

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Q: 2x - 3x + 13x+a if x#2 f(x) = . X-2 b if x = 2

A: Solution:- It is give that f(x) is continuous at x=2  and the given function is  f(x)=…

Q: Find max and min of function on the interval    f(x)=-x4-x3+5x2-4 on [-2,1]

A: The given function is; f(x)=-x4-x3+5x2-4 on [-2,1]

Q: Let f(x) = { *, if x= 2 ; for the eax if x + 2 function to be continuous at x = 2 the value of a is

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Q: A+b+c=180 (For c)

A: Given, A+b+c = 180 To be solved for c

Q: Let f and g are two real valued functions defined respectively by f(x) = 2x+1, g(x) = x^2-5. Find…

A: Given functions are f(x)=2x+1 and g(x)=x2-5. substitute the given functions in (f+g)x=f(x)+g(x).…

Q: What is an example of a function f : [-2, 2]-->R which is not differentiable at -1 but which is…

A: To find an example of a function                                   f : [-2, 2]→R which is not…

Q: If  f′(x) < 0 for 1 <x< 6, then f is decrescent over(1,6) True or false and why

A: If  f′(x) &lt; 0 for 1 &lt;x&lt; 6, then f is decrescent over (1,6) True or false and why

Q: Find the constants a and b such that the function is continuous on the entire real line x 3 a = b =

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Q: 11. g 13. F(r) = 3 r

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Q: Show that f (−1) = f (1), but that there is no point in (−1, 1) where f (0) is zero. Why does this…

A: Given: fx=1-x2/3 So, f-1=1--12/3=1-1=0 Also, f1=1-12/3=0 Thus, f-1=f1

Q: The function f(x) = x^2 is decrea sin g on (- ∞,0)  True or False

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Q: Are these functions injective or surjective?  f : R → R; f(x) = x^2,  f : R → Z; f(x) = bxc,  f :…

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Q: Prove that the following function is continuous on the interval [-5,5]: H(x)= the square root of…

A: Given, H(x)=25-x2we have to prove that the given function is continous on the interval[-5,5]…

Q: How many continuous functions f are there which satisfy (f(x))² = x² for all x?

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Q: Sketch the graph of f(x) = x2 - 9, x =< 4 f(x) = 8x - 25, x =< 4 Is f(x) continuous at x=4?…

A: To check: Whether the functions f(x) = x2 - 9, x≤4 and f(x) = 8x - 25, x≤4or not. . Solution: Sketch…

Q: x -1 f (x): x² +3x %3D

A: If two functions f,g are continuous then the function f+g,f-g,fg are also continuous. The function…