Question

What is the domain for g(x) = (6 + x)(4 + x).

Answer 1

The function g (x ) = (6 + x )(4 + x ).

From foil method : (a + b )(c + d ) = ac + bc + ad + bd.
g (x ) = 24 + 4x + 6x + x ^2

g (x ) =  x ^2 + 10x + 24.

The above equation represents the parabola.

We know that the parabola like curve.

The parabola giving us all real numbers is the domain, means, domain is (-∞,∞).

Therefore, domain of the given equation is (-∞,∞).

Answer 2

The function g (x ) = (6 + x )(4 + x ).

From foil method : (a + b )(c + d ) = ac + bc + ad + bd.
g (x ) = 24 + 4x + 6x + x ^2

g (x ) =  x ^2 + 10x + 24.

Domain of a function g (x) is a set of those values of x which will make the function mathematically legal or correct..certain operations like division by zero , square root of a negative number do not exist in real maths.

1. Domain excludes x - values that result in division by zero.

2. Domain excludes x - values that result in even roots of negative numbers.

The function g (x ) = x ^2 + 10x + 24 is a quadratic or parabola function.There are no rational or radical expressions, so there is nothing that will restrict the domain. Any real number can be used for x to get a meaningful output.

The domain of g (x ) = x ^2 + 10x + 24 is all real numbers.