Question

Let f(x) = x² and g(x) = ^x+1

____

^x+3

1. Evaluate(f °g)(2)

2. Find formular for (f ° g) (x)

Answer 1

1.

$$(f\circ g)(x)=(\dfrac{x+1}{x+2})^2$$

$$(f\circ g)(2)=(\dfrac{2+1}{2+2})^2=\dfrac{9}{16}$$

2.

$$(f\circ g)(x)=(\dfrac{x+1}{x+2})^2=\dfrac{(x+1)^2}{(x+2)^2}, x\not=-2$$