Algebra Examples

$f (x) = \frac{1}{4} x^{2}$ , $g (x) = - 2 x^{2}$ , $h (x) = 4 x^{2}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

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

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $- 2 x^{2}$ .

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

Step 3.2

Raise $- 2$ to the power of $2$ .

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

Step 4

Cancel the common factor of $4$ .

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Step 4.1

Factor $4$ out of $4 {(x^{2})}^{2}$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 5.2

Multiply $2$ by $2$ .

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