Example 15. Given the function { if x <1 3 – ba?, if x > 1, ax + 1, f(x) = find the real constants a and b such that the function f is continuous and differentiable at x = 1.

Q: 3. If f(x) = x + 1, find f(3) and f(- 3). Is f a one-to-one function?

A: The given function is fx=x2+1

Q: Let f be a function of x. Then f (10x) = 10 (f (x)). O True O False

A: the answer for the above statement is false. the explanation is given in the below step

Q: Let f(x) = x2 + 1 and g(x) = x + 2 be functions from R to R. If f(g(x)) = x2 + Ax + B and g(f(x))…

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Q: Each function f is defined as f :R +R. Prove why each of the functions is one to one or not c one.…

A: We will check the one to one of these functions

Q: 2) Let f be a function given by (3x +2 if f(x) = { 3 (x² + 1_ if Find f(0), f(-2), ƒ(-1), ƒ(1) and…

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Q: REVIEW: The range of basic sine and cosine functions -15 sin 0 s1 and 1s cos 0 S 1 - #3 For 0 sx <…

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Q: 2. Let a, b be real numbers for which b > a. Let functions f,9,h be defined on a domain [a, b] in…

A: Solution is here

Q: Let f be a function of x. f (x) = (x – 3)4 is an even function. - O True O False

A: Solution: The objective is to determine whether the given function is even or not

Q: The table contains some input-output pairs for the functions f and g. æ| f(x) | g(x) 2 2 9 6 9 3 9.…

A: To evaluate the given expression with the given table values.

Q: The function f and g are defined as follows. A. -3 or f(x)%= In(x+1), x>-1 8(x)=x² +2x , x>-1 B. -3…

A: Solved below

Q: Let f(x) ƒ¯¹(-4)= = x+1 x+8

A:

Q: Show that Rolle’s theorem is false for the function f(x) = |x| on the interval [−2, 2]. How can a…

A: Given function f(x)=|x|interval [-2,2] We apply Rolle's theorem only when the function is continuous…

Q: Which of the following functions are even? □ y = f(x)g(x) f(x) y = 12g(x) y = f(x) = g(x) y = g(x)¹3…

A: Here f and g are both odd.

Q: Example. For which values a and b is the following function continuous every where x² - a if x 2.

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Q: 4. Determine whether the following functions are one-to-one: a) f (x) = "+1 for all real numbers x +…

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Q: If Rolle's Theorem hold for the function f(x) = x3 + ax2 + bx in the interval 1 xs 2 at the point 4…

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Q: Given two functions f and g. Suppose that f is defined by f(x) = 1 if x + -1 if x: I+1 -1 and g(x) =…

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