Consider the following functions. f(x) = x − 3, g(x) = |x + 3| Find (f...

Consider the following functions. f(x) = x − 3, g(x) = |x + 3|

Find (f ∘ g)(x).

Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.)

Find (g ∘ f)(x).

Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.)

Find (f ∘ f)(x).

Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.)

Find (g ∘ g)(x).

Find the domain of (g ∘ g)(x). (Enter your answer using interval notation.)

Expert Solution

milcah answered 2 years ago

a) Find the value of the Wronskian of the functions f = x^7 and g = x^8...

a) Find the value of the Wronskian of the functions f = x^7 and g = x^8 at the piont x = 1. b) Let y be the solution of the equation y ″ − 5 y ′ + 6 y = 0 satisfying the conditions y ( 0 ) = 1 and y ′ ( 0 ) = 2. Find ln ⁡ ( y ( 1 ) ). c) Let y be the solution of the equation y ″ + 2 y ′...

Let f(x) = 5x+3 and g(x) =2x-5. Find (f+g)(x),(f-g)(x),(fg)(x), and (f/g) (x). Give the domain of...

Let f(x) = 5x+3 and g(x) =2x-5. Find (f+g)(x),(f-g)(x),(fg)(x), and (f/g) (x). Give the domain of each. (f+g) (x) = (f-g)(x) = (fg)(x) = (f/g)(x) = The domain of f+g is_ The domain of f-g is_ The domain of fg is _ The domain of f/g is _ Please at the end provide showed work.

3. Find the Fourier integral representation of each of the following functions. f(x) = sin(x)/x

Find all functions f(x) with f′′(x) = 3x^3 − 2x^2 + x, f(0) = 1, and...

Find all functions f(x) with f′′(x) = 3x^3 − 2x^2 + x, f(0) = 1, and f(1) = 1.

For f(x)=9x+5 and g(x)=x2 find the following composite functions and state the domain of each a)...

For f(x)=9x+5 and g(x)=x2 find the following composite functions and state the domain of each a) f o g b) g o f c) f o f d) g o g a. the domain of f o g is b. (g o f )(x)= a. the domain of g o f is c. ( f o f )(x)= the domain of f o f is d. ( g o g)(x)= the domain of g o g is

1. Find the critical numbers for the following functions (a) f(x) = 2x 3 − 6x...

1. Find the critical numbers for the following functions (a) f(x) = 2x 3 − 6x (b) f(x) = − cos(x) − 1 2 x, [0, 2π] 2. Use the first derivative test to determine any relative extrema for the given function f(x) = 2x 3 − 24x + 7

f(x) = −x2 + 3x and g(x) = x − 3 Find the area of the...

f(x) = −x2 + 3x and g(x) = x − 3 Find the area of the region completely enclosed by the graphs of the given functions f and g in square units.

If f(x) = exg(x), where g(0) = 3 and g'(0) = 4, find f '(0).

If \(f(x)=e^{x} g(x),\) where \(g(0)=3\) and \(g(0)=4,\) find \(f(0)\)

if f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x).

if f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x) (a) Find u'(1) (b) Find v'(5).

For the following functions f and g : f(x, y) = e ax − (1 −...

For the following functions f and g : f(x, y) = e ax − (1 − a)lny a > 0 g(x, y, z) = −3x 2 − 3y 2 − 3z 2 + 2xy + 2xz + 2yz 1. Calculate the Hessian matrices of f and g noted Hf (x, y) and Hg(x, y, z) 2. Show that Hg(x, y, z) is define negativly for all (x, y, z) ∈ Dg 3. For what value o a is , Hf...

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