Question

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

Answer 1

Answer:

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

Step-by-step 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

$\frac{f}{g} = \frac{3-x^{2} }{x^{2} + 2x - 15}$

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.

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

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