`If p(x)=x+3,then p(x) +p(-x) is equal to:

Options

A. 3
B. 2x
C. 0
D. 6

Explanation

`x=f(t)=a^(In(b))=a^(t" In "b)" (1)"`
`y=g(t)=b^(-In(a^(t)))=(b^(In a))^(-t)=(a^(In b))^(-t)=a^(-t" In b")`
`therefore" "y=g(t)=a^(In(b^(-t)))=f(-t)" (2)"`
From equations (1), and (2),
`xy=1`
`y=(1)/(x)`
`therefore" "(dy)/(dx)=-(1)/(x^(2))=-(1)/(f^(2)(t))`
`"Also, "xy=1 rArr-(1)/(f^(2)(t))=-g^(2)(t)`
`therefore" "(dy)/(dx)=-(1)/(x^(2))=-(y^(2))/(1)`
`"Also, "xy=1 rArr(dy)/(dx)=-(y)/(x)=-(g(t))/(f(t))`