Precalculus Examples

$j (x) = \sqrt{x + 6}$ $k (x) = 9 - x$ Find $j (k (11))$

Step 1

Set up the composite result function.

$j (k (x))$

Step 2

Evaluate $j (9 - x)$ by substituting in the value of $k$ into $j$ .

$j (9 - x) = \sqrt{(9 - x) + 6}$

Step 3

Add $9$ and $6$ .

$j (9 - x) = \sqrt{- x + 15}$

Step 4

Evaluate the result function by replacing $x$ with $11$ in the function.

$\sqrt{- (11) + 15}$

Step 5

Simplify the evaluated function.

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Step 5.1

Multiply $- 1$ by $11$ .

$\sqrt{- 11 + 15}$

Step 5.2

Add $- 11$ and $15$ .

$\sqrt{4}$

Step 5.3

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2}}$

Step 5.4

Pull terms out from under the radical, assuming positive real numbers.

$2$