Question

What is the domain of f/g? f(x) = 3-x^2 and g(x) = x^2 +2x -15​

Answer 1

Domain = (-infinity, -5) U (-5,3) U (3, +infinity)

Explanation:

Step 1: Write the two functions

`f(x) = 3 - x^(2) \\g(x) = x^(2) + 2x - 15`

Step 2: Write the expression for a function f/g

`(f)/(g) = (3-x^(2) )/(x^(2) + 2x - 15)`

Step 3: Find the domain of the function f/g

Domain of a function are set of input values for which the function is real and defined

First equate the denominator to zero.

`x^(2) +2x - 15 = 0\\factor it\\x^(2) + 5x - 3x - 15 = 0\\x(x+5) - 3(x + 5) = 0\\(x - 3)(x + 5) = 0\\x = 3 0r -5`

`domain = (-infinity, -5) U (-5,3) U (3, +infinity)`