Algebra Examples

$f (x) = \frac{3}{x - 4}$ , $g (x) = \frac{3}{x} + 4$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{3}{x - 4})$ by substituting in the value of $f$ into $g$ .

$g (\frac{3}{x - 4}) = \frac{3}{\frac{3}{x - 4}} + 4$

Step 3

Simplify each term.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$g (\frac{3}{x - 4}) = 3 (\frac{x - 4}{3}) + 4$

Step 3.2

Cancel the common factor of $3$ .

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Step 3.2.1

Cancel the common factor.

$g (\frac{3}{x - 4}) = 3 (\frac{x - 4}{3}) + 4$

Step 3.2.2

Rewrite the expression.

$g (\frac{3}{x - 4}) = x - 4 + 4$

Step 4

Combine the opposite terms in $x - 4 + 4$ .

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Step 4.1

Add $- 4$ and $4$ .

$g (\frac{3}{x - 4}) = x + 0$

Step 4.2

Add $x$ and $0$ .

$g (\frac{3}{x - 4}) = x$