Consider the functions c( ) 3 sin osx xf x += where 0 ≤ x ≤ π and g (x) = 2x where x ∈  .(a) Find ( f  g)(x) .

Consider the following functions:𝑓(𝑥)=sin⁡(𝑥4−𝑥2)ℎ(𝑥)=(∣𝑥∣−3)3𝑔(𝑥)=ln⁡(∣𝑥∣)+3𝑠(𝑥)=sin⁡3(𝑥)​ f(x)=sin(x 4 −x 2 )h(x)=(∣x∣−3) 3 g(x)=ln(∣x∣)+3s(x)=sin 3 (x)​ Which of the following is true?A.h and g are even, f and s are odd.B. f is even, h and s are odd.C.h and s are even, f is odd.D. f, h, and s are odd.E. f and h are even, s is odd.SUBMITarrow_backPREVIOUS

Consider the function f: R→R defined by f(x)=sin(x)+cos(2x). Which of the following statements about f(x) is true?

g(x) :=(x sin(1/x) if x > 0,3 if x = 0

(b) Find the exact value of ( )cos p q+ .6. Functions f and g are defined on R by• ( ) 2 5f x x= +• ( ) 2 2g x x x= − .(a) Find an expression for ( )( )f g x .(b) Find an expression for ( )( )g f x .(c) Express ( )( ) ( )( )g f x f g x− in the form ( )2a x b c+ + .123214

Show that the following functions are differentiable at x = 0.(a) |x| sin x (b) x2/3 sin x (c) 3√x(1−cos x) (d) h(x) ={x2 sin(1/x), x 6 = 00, x = 0.Page 3