Question

What will be the composition of two functions f ° g from R to R,

(a)

f(x) = 2x + 3, g(x) = 3x + 2

(b)

f(x) = 2x + 3, g(x) = sin (x)

(c)

f(x) = sin (x), g(x) = 2x + 3

(d)

f(x) = sin (x), g(x) = x2

(e)

f(x) = |x|, g(x) = 2x + 3

Answer 1

a)

$$f\circ g=2(3x+2)+3$$

$$f\circ g=6x+7$$

b)

$$f\circ g=2\sin x+3$$

c)

$$f\circ g=\sin (2x+3)$$

d)

$$f\circ g=\sin (x^2)$$

e)

$$f\circ g=|2x+3|$$