Question

In: Math

Use f(x) = ?2x, g(x) = square root of x and h(x) = |x| to find...

Use f(x) = ?2x, g(x) = square root of x and h(x) = |x| to find and simplify expressions for the following functions and state the domain of each using interval notation. a . (h ? g ? f)(x) b. (h ? f ? g)(x) (g ? f ? h)(x)

Expert Solution

a) h o go f(x)

we can write this as, h o g(f(x)) = h o g(-2x)

h (g(-2x)) = h ( )

h ( ) =

in order to get the square root term positive, x must be negative. So, domain of the function

b. (h ? f ? g)(x)

h o f (g(x)) = h o f ()

= h ( f() = h()

= =

=

All non-negative numbers can be of domain. So,

c. (g ? f ? h)(x)

g(f(h(x))) = g(f()

= g()

=

In this case, the function is not having a domain as only x = 0.

milcah answered 1 year ago

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a =...

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a = 0. Lf (x) = Lg(x) = Lh(x) = (b) Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain. The linear approximation appears to be the best for the function ? f g h since it is closer to ? f g h for a larger domain than it is to - Select - f and g g and h f and h . The approximation looks worst for ? f g h since ? f g h moves away from L faster...

Use the secant Method to find a root for the function: f(x) = x^3 + 2x^2...

Use the secant Method to find a root for the function: f(x) = x^3 + 2x^2 + 10x -20, with x_0 = 2, and x_1 = 1.

Differentiate the following: 1) f(x) = √2x-4. (all under square root) 2) f(x) = x/5-x 3)...

Differentiate the following: 1) f(x) = √2x-4. (all under square root) 2) f(x) = x/5-x 3) y=cos(4x^3) 4) f(x)=tan(x^2) 5) f(x)= 3e^2x cos(2x) 6) y= sin2x/cosx 7) y= √sin(cosx) (all under the square root)

Find the domain of the function g(x) = square root of 3x+3

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.

Use the Fixed-Point Iteration Method to find the root of f ( x ) = x...

Use the Fixed-Point Iteration Method to find the root of f ( x ) = x e^x/2 + 1.2 x - 5 in the interval [1,2].

Consider the root of function f(x) = x 3 − 2x − 5. The function can...

Consider the root of function f(x) = x 3 − 2x − 5. The function can be rearranged in the form x = g(x) in the following three ways: (a) x = g(x) = x3 − x − 5 (b) x = g(x) = (x 3 − 5)/2 (c) x = g(x) = thirdroot(2x + 5) For each form, apply fixed-point method with an initial guess x0 = 0.5 to approximate the root. Use the error tolerance = 10-5 to...

Question

Use f(x) = ?2x, g(x) = square root of x and h(x) = |x| to find...

Solutions

Expert Solution

Related Solutions