If f(x) = x² - 1 and g(x) = 2x - 3, what is the domain of g(f(x))?

Solution:

Given: Functions are 

f(x) = x² - 1

g(x) = 2x - 3

To find domain of g(f(x))

g(f(x)) = g(x² - 1)

Substituting it, we get

g(f(x)) = 2(x² - 1) - 3

By further calculation

g(f(x)) = 2x² - 2 - 3

So we get,

g(f(x)) = 2x² - 5

The function has no undefined points or domain constraints. The domain of g(f(x)) is the output given by f(x).

The composite function g(f(x)) takes all its inputs as the outputs of the function f(x).

Therefore, the domain is -∞< x < +∞.

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If f(x) = x² - 1 and g(x) = 2x - 3, what is the domain of g(f(x))?

Summary:

If f(x) = x² - 1 and g(x) = 2x - 3, then the domain of g(f(x)) is -∞< x < +∞.