Question

What is the domain for f(x) = 2(x - 5)^2 - 8.

Answer 1

The function is f (x ) = 2(x - 5)^2 - 8.

Let  f (x ) = y = 2(x - 5)^2 - 8.

Compare the above equation y = 2(x - 5)^2 - 8 with standard from from the of the equation of a parabola with vertex (h, k ) and axis of symmetry x = h is y = a(x - h )^2 + k.

Vertex (h, k ) = (5, - 8) and axis of symmetry h = 5.

So, the given function 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 is f (x ) = 2(x - 5)^2 - 8.

Domain of a function f (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 f (x ) = 2(x - 5)^2 - 8 is a 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 f (x ) = 2(x - 5)^2 - 8 is all real numbers.