Question

X2+4x+6

a.f(-8) b. f(x+4) c.f(-x)

Answer 1

a. f(-8) = 38

b. f(x + 4) = x² + 12x + 38

c. f(-x) = x² - 4x + 6

Explanation:

`f(x)=x^2+4x+6\\\\a.\\f(-8)-\text{put x = -8 to the equation}\\\\f(-8)=(-8)^2+4(-8)+6=64-32+6=38\\\\b.\\f(x+4)-\text{exchange x to x + 4}\\\\f(x+4)=(x+4)^2+4(x+4)+6\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\ \text{and}\ \text{distributive property}\\\\f(x+4)=x^2+2(x)(4)+4^2+4x+(4)(4)+6\\\\f(x+4)=x^2+8x+16+4x+16+6\\\\\text{combine like terms}\\\\f(x+4)=x^2+(8x+4x)+(16+16+6)\\\\f(x+4)=x^2+12x+38`

`c.\\f(-x)-\text{exchange x to -x}\\\\f(-x)=(-x)^2+4(-x)+6=x^2-4x+6`