Algebra Examples

$f (x) = 3 x^{2}$ , $g (x) = \frac{1}{2} x^{2}$ , $h (x) = - 2 x^{2}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (\frac{1}{2} x^{2}) = 3 {(\frac{1}{2} x^{2})}^{2}$

Step 3

Combine $\frac{1}{2}$ and $x^{2}$ .

$f (\frac{1}{2} x^{2}) = 3 {(\frac{x^{2}}{2})}^{2}$

Step 4

Simplify the expression.

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Step 4.1

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

$f (\frac{1}{2} x^{2}) = 3 (\frac{{(x^{2})}^{2}}{2^{2}})$

Step 4.2

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

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Step 4.2.1

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

$f (\frac{1}{2} x^{2}) = 3 (\frac{x^{2 \cdot 2}}{2^{2}})$

Step 4.2.2

Multiply $2$ by $2$ .

$f (\frac{1}{2} x^{2}) = 3 (\frac{x^{4}}{2^{2}})$

Step 4.3

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

$f (\frac{1}{2} x^{2}) = 3 (\frac{x^{4}}{4})$

Step 5

Combine $3$ and $\frac{x^{4}}{4}$ .

$f (\frac{1}{2} x^{2}) = \frac{3 x^{4}}{4}$