Precalculus Examples

If $f (x) = 2 x$ and $g (x) = 2 x^{2} - 1$ find $f (g (x))$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (2 x^{2} - 1)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Apply the distributive property.

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

Step 4

Multiply.

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Step 4.1

Multiply $2$ by $2$ .

$f (2 x^{2} - 1) = 4 x^{2} + 2 \cdot - 1$

Step 4.2

Multiply $2$ by $- 1$ .

$f (2 x^{2} - 1) = 4 x^{2} - 2$