Precalculus Examples

$f (x) = \frac{x - 3}{5}$ , $g (x) = 5 x + 3$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{x - 3}{5})$ by substituting in the value of $f$ into $g$ .

$g (\frac{x - 3}{5}) = 5 (\frac{x - 3}{5}) + 3$

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Cancel the common factor.

$g (\frac{x - 3}{5}) = 5 (\frac{x - 3}{5}) + 3$

Step 3.2

Rewrite the expression.

$g (\frac{x - 3}{5}) = x - 3 + 3$

Step 4

Combine the opposite terms in $x - 3 + 3$ .

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Step 4.1

Add $- 3$ and $3$ .

$g (\frac{x - 3}{5}) = x + 0$

Step 4.2

Add $x$ and $0$ .

$g (\frac{x - 3}{5}) = x$