Find the Domain of the Composition f(g(x)) f(x)=x+2 , g(x)=4x^2-7x-2

$f (x) = x + 2$ , $g (x) = 4 x^{2} - 7 x - 2$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (4 x^{2} - 7 x - 2)$ by substituting in the value of $g$ into $f$ .

$f (4 x^{2} - 7 x - 2) = (4 x^{2} - 7 x - 2) + 2$

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+2 , g(x)=4x^2-7x-2

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