fx x2 16 and gx x 4 Find fg and its domain A x 4 all rea

f(x) = x^2 -16 and g(x) = x + 4. Find f/g and its domain A. x - 4; all real numbers except x notequalto 4 B. x - 4; all real numbers except x notequalto -4 C. x + 4; all real numbers except x notequalto 4 D. x + 4; all real numbers except x notequalto 4

Solution

f(x) =x^2 -16

g(x) =x+4

f/g = (x^2 -16)/(x+4)

we know that a^2 -b^2 = (a-b)(a+b)

here (x^2 -16) can be written as ((x)^2 -(4)^2) which can be written as (x-4)(x+4)

Therefore f/g = ((x-4)(x+4))/(x+4)

f/g = x-4

and domain of f/g will be x not equal to -4 as in denominator (x+4) is there which will make it undefined for that value.

so f/g =x-4 and domain is all real numbers except x =-4

so option b is correct .

Thank you