Assume that f (x) and g(x) are both differentiable functions on some interval I; in addition, assume that f(x) and g(x) are increasing on I. Let h(x) = f(g(x)). Show that h(x) is also increasing on I. (Note: This is a generalization of Q4, where you are not given a specific f or g.)

Q: 1+x is even, odd, or neither. Show your work. |x| 2. Determine whether the function fx) = %3D

A:

Q: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that f…

A: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that…

Q: Suppose f is differentiable on the set of real numbers R and a E R. Let F(x)= f(xª) and G(x) =…

A: F(x)=f(xα)F'(x)=f'(xα)ddx(xα) , [chain…

Q: f(x) = x + 1 √x

A: Given data

Q: Let f be the function given by f(x) = Jax + b for x 2 where a and b are constants

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Q: Consider the following piecewise-defined function: f(x) = { 4-ax² if x ≤1 b 2x if x > 1 Find the…

A: Ans :Now we need to sketch the graph in the interval [-3,3]Firstly let's find some points on the…

Q: find functions f and g so that f ∘ g = H.

A: given: Hx=1-x2 we have to find the functions f and g so that f ∘ g = H.

Q: The function x2 f(x) = 1 - x is decreasing on (0, 1). Select one: O True O False

A:

Q: Given functions f : R → R and g : R → R. Suppose that g ◦ f turns out as g ◦ f(x) =| x^2 + 7 |.…

A:

Q: Consider the function f(t) = = -X 3-x (x − 3)² - if x 3

A:

Q: 2 Let f(x)=Vx and g(x)=- x-4

A: Given that  f(x)=√x and g(x)=2/(x-4) To find the f of g

Q: Let f:Z+ à Z+ be defined as f(x)=x3 a. Draw a graph of the function by calculating the values of…

A: Let f be a function, f: ℤ+ → ℤ+ Then f(x)=x3 a. Let x be a positive integers, that is x=0,1,2,3,..…

Q: Let h be a function with h1(10)=-12, and let g(x)=h(x2+1). Find g1(3).

A: Given:  h'10=-12, gx=hx2+1 Find:g'3 As,   gx=hx2+1 Using Composition of functions and the derivative…

Q: B. Determine whether f(x) (x - 3) (2x + 1) (x + 4) is continuous at x= 3.

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Q: Let ƒ(x) = x/x - 2. Find a function y = g(x) so that (ƒ ∘ g)(x) = x.

A:

Q: Show whether f(x) is continuous (3х-2 f(x)={ x-2 x² -4 for x=- for x+ -

A: Given that, f(x) = 3x - 2; for x = - 2 f(x) = (x + 2)/(x^2 - 4); for x not equal to - 2 So when x is…

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

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Q: Since f(x) is continuous between a and b, the function needs to cross the x-axis. O TRUE O FALSE O…

A: Given fx is continuous between a and b

Q: Define H(x) as a piecewise defined function and evaluate H(1), H(2), H(3), H(0) and H(-2) given by,…

A: We know, x = -x,x<0x,x≥0

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.