Show that the function f : R → R given by f(x) = x/(1+|x|) is increasing.

Q: Let f(x) f-¹(x) = 1 x + 11

A: we need to find the inverse of the function.

Q: Draw the graph of the function f :R → R defined by f (x) = x3, x∈R.

A: We will make a table for f(x)=x3 x -1 0 1 y -1 0 1

Q: Define g(-5) in a way that extends g(x) = x² - 25 x + 7x + 10 to be continuous at x = -5.

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Q: Consider the function f(x) х — 2 х — 4*

A: The solution are next step

Q: determine the continuity of the function at a.

A: The objective of this question is to determine whether the function f(x) = 1/(x + 2) is continuous…

Q: Define g(-5) in a way that extends g(x)= 9(-5) = x² - 25 x + 8x + 15 to be continuous at x = -5.

A: We have to define g(-5) such that g(x) is continuous at x = -5.

Q: f: Z4 → Z5 f([a]4) [39]s if a > 0. =

A: Introduction: A well-defined function is a function that is unambiguously specified by its…

Q: Find the graph of the function f(x) = [x] + [x/2] from R to R.

A: Given function is fx=x+x2. Definition: Floor function is the greatest integer that is less than or…

Q: Suppose f and g are positive functions. Is the following true or false? Vf,g:N → R f(x) E O(g(x)) =…

A: Big-Θ notation: A function g(n) is in Θ(f(n)) if there exist constants c1, c2, and N such that…

Q: Let f(x) = ln x and g(x) Show that f(x) and g(x) are both increasing when x > 0. Vr.

A: Given, f(x) = lnx When f(x) is increasing then f'(x) > 0  Differentiating f(x) with respect to x…

Q: 1. Describe all functions f such that f(r) ar² + bx +c and f(1) = 2 and f(-1) = 6.

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Q: Consider the function f : RH→ R defined by f(x) = 2e(2z+5) log(2r+5) + If f convex or concave ? Why…

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Q: Let f(x) ƒ-¹(x) = = 1 x + 13

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Q: Find a function f(1) such that | f(z)dr= 2² – 5.

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Q: Let f (x) = x2 − 2x. Determine a domain on which f−1 exists, and find a formula for f−1 for this…

A: The given function is

Q: Examine whether the following function is Analytic or not f(z) = [z]²

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