Algebra Examples

$f (x) = \frac{1}{23 x - 1}$ , $g (x) = \frac{1}{x^{2}}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (\frac{1}{x^{2}}) = \frac{1}{23 (\frac{1}{x^{2}}) - 1}$

Step 3

Simplify the denominator.

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Step 3.1

Combine $23$ and $\frac{1}{x^{2}}$ .

$f (\frac{1}{x^{2}}) = \frac{1}{\frac{23}{x^{2}} - 1}$

Step 3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{x^{2}}{x^{2}}$ .

$f (\frac{1}{x^{2}}) = \frac{1}{\frac{23}{x^{2}} - 1 \cdot \frac{x^{2}}{x^{2}}}$

Step 3.3

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

$f (\frac{1}{x^{2}}) = \frac{1}{\frac{23}{x^{2}} + \frac{- x^{2}}{x^{2}}}$

Step 3.4

Combine the numerators over the common denominator.

$f (\frac{1}{x^{2}}) = \frac{1}{\frac{23 - x^{2}}{x^{2}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{1}{x^{2}}) = 1 (\frac{x^{2}}{23 - x^{2}})$

Step 5

Multiply $\frac{x^{2}}{23 - x^{2}}$ by $1$ .

$f (\frac{1}{x^{2}}) = \frac{x^{2}}{23 - x^{2}}$