Find the Domain of the Composition f(g(x)) f(x)=2x^2+x-3 and g(x)=x-1

$f (x) = 2 x^{2} + x - 3$ and $g (x) = x - 1$

Set up the composite result function.

$f (g (x))$

Evaluate $f (x - 1)$ by substituting in the value of $g$ into $f$ .

$f (x - 1) = 2 {(x - 1)}^{2} + x - 1 - 3$

Remove parentheses.

$2 {(x - 1)}^{2} + x - 1 - 3$

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Find the Domain of the Composition f(g(x)) f(x)=2x^2+x-3 and g(x)=x-1

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