The differentiable functions f and g are defined for all real numbers x. Values of f, f', g, and g' for various values of x are given in the table. x f(x) f'(x) g(x) g'(x) 4 8 25 -5 8 5 3 16 6 2 If D(x) = F²(x) what is the value of D'(4)? x 7274 о 1 72 O

Q: [6] Use the algebraic test to determine if these functions are odd, even, or neither. [Odd: f(-x) =…

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Q: If f is one-to-one and f( – 3) = 12, then f-'(12) and (f( – 3))¯

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Q: The one-to-one functions g and h are defined as follows. g={(-9, -1), (-2, 1), (1, –3), (4, 2)} h…

A: The given function g and h are one-one function which is defined as a function for which every…

Q: b) The difference of two real-valued functions f and is defined by f – g := f + const_1 · g. That…

A: b) We want to express the given definition of the function in terms of two indicator functions. Let…

Q: Suppose f and g are one-to-one functions such that f(2) = 7, f(4) = 2, and g(2) = 5. Find the value,…

A: We have given functions f and g are one-to-one. Then, a. gof-17=gf-17=g2=5 b. fog-15=fg-15=f2=7

Q: 4) Find fog, gof , f+g and fg where f (x) = x^2 + 1 and g(x) = x + 2, are functions from R to R

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Q: t is the direction of fastest increase at (-3, 4, -4) for the function f(x, y, z) = 1 x² + y² + z²

A: We have to find the direction of faster increase at (-3,4,-4)

Q: If f(x) = x + 3 and g(x) = x – 3, (a) f(g(x)) : (b) g(f(x)) = (c) Thus g(x) is called an function of…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 2. The zeros of a function f(x) are 3 and 4, while the zeros of a second function g(x) are 3 and 7.…

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