Find f(g(x)) f(x)=6x-3 g(x)=1/6(x+3)

$f (x) = 6 x - 3$ $g (x) = \frac{1}{6} (x + 3)$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{1}{6} \cdot (x + 3))$ by substituting in the value of $g$ into $f$ .

$f (\frac{1}{6} \cdot (x + 3)) = 6 (\frac{1}{6} \cdot (x + 3)) - 3$

Step 3

Simplify each term.

Apply the distributive property.

$f (\frac{1}{6} \cdot (x + 3)) = 6 (\frac{1}{6} x + \frac{1}{6} \cdot 3) - 3$

Combine $\frac{1}{6}$ and $x$ .

$f (\frac{1}{6} \cdot (x + 3)) = 6 (\frac{x}{6} + \frac{1}{6} \cdot 3) - 3$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$f (\frac{1}{6} \cdot (x + 3)) = 6 (\frac{x}{6} + \frac{1}{3 (2)} \cdot 3) - 3$

Cancel the common factor.

$f (\frac{1}{6} \cdot (x + 3)) = 6 (\frac{x}{6} + \frac{1}{3 \cdot 2} \cdot 3) - 3$

Rewrite the expression.

$f (\frac{1}{6} \cdot (x + 3)) = 6 (\frac{x}{6} + \frac{1}{2}) - 3$

Apply the distributive property.

$f (\frac{1}{6} \cdot (x + 3)) = 6 (\frac{x}{6}) + 6 (\frac{1}{2}) - 3$

Cancel the common factor of $6$ .

Cancel the common factor.

$f (\frac{1}{6} \cdot (x + 3)) = 6 (\frac{x}{6}) + 6 (\frac{1}{2}) - 3$

Rewrite the expression.

$f (\frac{1}{6} \cdot (x + 3)) = x + 6 (\frac{1}{2}) - 3$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$f (\frac{1}{6} \cdot (x + 3)) = x + 2 (3) (\frac{1}{2}) - 3$

Cancel the common factor.

$f (\frac{1}{6} \cdot (x + 3)) = x + 2 \cdot (3 (\frac{1}{2})) - 3$

Rewrite the expression.

$f (\frac{1}{6} \cdot (x + 3)) = x + 3 - 3$

Step 4

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

Subtract $3$ from $3$ .

$f (\frac{1}{6} \cdot (x + 3)) = x + 0$

Add $x$ and $0$ .

$f (\frac{1}{6} \cdot (x + 3)) = x$