Find f(g(x)) f(x)=6x-15 and g(x)=1/6x+5/2

$f (x) = 6 x - 15$ and $g (x) = \frac{1}{6} x + \frac{5}{2}$

Set up the composite result function.

$f (g (x))$

Evaluate $f (\frac{1}{6} x + \frac{5}{2})$ by substituting in the value of $g$ into $f$ .

$f (\frac{1}{6} x + \frac{5}{2}) = 6 (\frac{1}{6} x + \frac{5}{2}) - 15$

Simplify each term.

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

$f (\frac{1}{6} x + \frac{5}{2}) = 6 (\frac{x}{6} + \frac{5}{2}) - 15$

Apply the distributive property.

$f (\frac{1}{6} x + \frac{5}{2}) = 6 (\frac{x}{6}) + 6 (\frac{5}{2}) - 15$

Cancel the common factor of $6$ .

Cancel the common factor.

$f (\frac{1}{6} x + \frac{5}{2}) = 6 (\frac{x}{6}) + 6 (\frac{5}{2}) - 15$

Rewrite the expression.

$f (\frac{1}{6} x + \frac{5}{2}) = x + 6 (\frac{5}{2}) - 15$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$f (\frac{1}{6} x + \frac{5}{2}) = x + 2 (3) (\frac{5}{2}) - 15$

Cancel the common factor.

$f (\frac{1}{6} x + \frac{5}{2}) = x + 2 \cdot (3 (\frac{5}{2})) - 15$

Rewrite the expression.

$f (\frac{1}{6} x + \frac{5}{2}) = x + 3 \cdot 5 - 15$

Multiply $3$ by $5$ .

$f (\frac{1}{6} x + \frac{5}{2}) = x + 15 - 15$

Combine the opposite terms in $x + 15 - 15$ .

Subtract $15$ from $15$ .

$f (\frac{1}{6} x + \frac{5}{2}) = x + 0$

Add $x$ and $0$ .

$f (\frac{1}{6} x + \frac{5}{2}) = x$