Find the Domain of the Composition f(g(x)) f(x)=x^3+12x^2+25x-70 g(x)=x+7

$f (x) = x^{3} + 12 x^{2} + 25 x - 70$ $g (x) = x + 7$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x + 7)$ by substituting in the value of $g$ into $f$ .

$f (x + 7) = {(x + 7)}^{3} + 12 {(x + 7)}^{2} + 25 (x + 7) - 70$

Step 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:

${x | x \in ℝ}$

Step 4

Find the Domain of the Composition f(g(x)) f(x)=x^3+12x^2+25x-70 g(x)=x+7

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