The antiderivative of f (x), which is F (x), exhibits an odd symmetry, i.e., it satisfies the property F ( – x) = – F (x). If | f(x) dr = K, determine which of the following is true . Assume both f (x) and F (x) are defined for all real values of x. A 1+xf (x) b -dx = - 2K + In] a '1+xf (x) (B -dr = K + In b В 1+xf (x) -dr = 2K + In b '1+xf (x) -dx = - K + In b D

Q: Define f (x) = 4+ x – x² and g(x) = 5x – 3. Define f(x) - - (f o g)(x) = (go f)(x). True False

A:

Q: Show that x – P VB + (d - x)* g(x) is a decreasing function of x.

A:

Q: Let f(x) = m1x + a and g(x) = m2x + b, where m1, m2, a, and b are constants. Determine the necessary…

A: f∘g=g∘ffgx=gfxfm2x+b=gm1x+am1m2x+b+a=m2m1x+a+bm1m2x+m1b+a=m1m2x+m2a+bm1b-b=m2a-abm1-1=am2-1

Q: Let f(x) = 3x – 1 and g(x) = 4 - x. Find all values of x for which f(x) < -1 or g(x) < -2.

A: Consider the function f(x)=3x-1 and g(x)=4-x. To find all values of x for which f(x)&lt;-1 or…

Q: Let f(x)=Ax³ + 2x2-16x +4. Find the value of A such that f(x) has a point of inflection when x =…

A: A function,

Q: Let f(x) = 2x – 5 and g(x) = 3 - x. Find all values of x for which f(x) 2 3 or g(x) < 0.

A: Given: fx=2x-5gx=3-x To Find:  All values of x for which fx≥3 or gx&lt;0

Q: Let ƒ(x) = 2x2 + 5x and g(x) = 4x + 1. Find g[f(x)]

A: Given: fx=2x2+5x . gx=4x+1 . gfx can be calculated by replacing the x by fx in the function gx as,…

Q: Find the value of c so that the function x² + cx if x 1 is continuous for all real numbers.

A:

Q: a. Determine whether f(x) = 5/(x+1) is a one-to-one function from R to R, if not, give a counter…

A:

Q: Express the function F in the form f ∘ g ∘ h. (Enter your answers as a comma-separated list. Use…

A: first we analysis to given question that how to find f, G, h then we compute F(x) function.

Q: Determine F(x) if, for all real x and y, F(x)F(y) – F(xy) = x + y.   Hint:  What could F(1) be?

A: Consider the provided question, We have to find F(x).

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

A: It is given that;  H(x)=x2+1 and; (f∘g)(x)=H(x)

Q: Define f (x) = Vx² + 1 and g(x) = 2 – x². Find and simplify (go f)(x).

A:

Q: Let f(x) f-¹(-2) = x + 3 x + 6

A:

Q: Suppose f is a real function satisfying f(x + f(x)) = 4ƒ(x) and ƒ(1) = 4. What is ƒ(21)? f(21)=

A: Suppose f is a real function satisfying f(x+ f(x))= 4f(x) and f(1) = 4, what is f(21)?

Q: 1. Let f(r) and g(a) 4x + 1. 4 Then (f o g)(6) (ƒ o g)(x)

A: We have to find function

Q: Express the function F in the form f∘g. (Enter your answers as a comma-separated list. Use…

A: Remark: we know that (f•g)(x) = f(g(x))

Q: Let f(x)=x2, g(x)=2x+5, and h(x)=x2-1 a. h[f(-2)] b. f[g(x-1)]

A: Given that , fx=x2 gx=2x+5 hx=x2-1

Q: Find the following for y = 5 tan(3x - 2) Period Phase shift Range

A:

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&lt;0x,x≥0