Question

F(x) = x + 6, g(x) = x − 6

(a) (f + g)(x) =



(b) (f − g)(x) =



(c) (fg)(x) =



(d) (f/g)(x) =

Answer 1

(a) To find (f + g)(x), we simply add the functions f(x) and g(x):

(f + g)(x) = (x + 6) + (x - 6)

Expanding the expression, we get:

(f + g)(x) = x + 6 + x - 6

Combining like terms, we have:

(f + g)(x) = 2x

So, (f + g)(x) = 2x.

(b) To find (f - g)(x), we subtract the function g(x) from f(x):

(f - g)(x) = (x + 6) - (x - 6)

Expanding the expression, we get:

(f - g)(x) = x + 6 - x + 6

Combining like terms, we have:

(f - g)(x) = 12

So, (f - g)(x) = 12.

(c) To find (fg)(x), we multiply the functions f(x) and g(x):

(fg)(x) = (x + 6)(x - 6)

Expanding the expression using the distributive property, we get:

(fg)(x) = x^2 - 6x + 6x - 36

Simplifying further, we combine like terms:

(fg)(x) = x^2 - 36

So, (fg)(x) = x^2 - 36.

(d) To find (f/g)(x), we divide the function f(x) by g(x):

(f/g)(x) = (x + 6) / (x - 6)

This is the simplified form of (f/g)(x).