Calculus Examples

$f (x) = x^{2} - 1$ , $g (x) = \sin (x)$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\sin (x))$ by substituting in the value of $g$ into $f$ .

$f (\sin (x)) = \sin^{2} (x) - 1$

Step 3

Simplify with factoring out.

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Step 3.1

Reorder $\sin^{2} (x)$ and $- 1$ .

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

Step 3.2

Rewrite $- 1$ as $- 1 (1)$ .

$f (\sin (x)) = - 1 \cdot 1 + \sin^{2} (x)$

Step 3.3

Factor $- 1$ out of $\sin^{2} (x)$ .

$f (\sin (x)) = - 1 \cdot 1 - 1 (- \sin^{2} (x))$

Step 3.4

Factor $- 1$ out of $- 1 (1) - 1 (- \sin^{2} (x))$ .

$f (\sin (x)) = - 1 (1 - \sin^{2} (x))$

Step 3.5

Rewrite $- 1 (1 - \sin^{2} (x))$ as $- (1 - \sin^{2} (x))$ .

$f (\sin (x)) = - (1 - \sin^{2} (x))$

Step 4

Apply pythagorean identity.

$f (\sin (x)) = - \cos^{2} (x)$