Find f(g(x)) f(x)=6/5x-7 , g(x)=(5x+35)/6

$f (x) = \frac{6}{5} x - 7$ , $g (x) = \frac{5 x + 35}{6}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{5 x + 35}{6})$ by substituting in the value of $g$ into $f$ .

$f (\frac{5 x + 35}{6}) = \frac{6}{5} \cdot (\frac{5 x + 35}{6}) - 7$

Step 3

Simplify each term.

Factor $5$ out of $5 x + 35$ .

Factor $5$ out of $5 x$ .

$f (\frac{5 x + 35}{6}) = \frac{6}{5} \cdot \frac{5 (x) + 35}{6} - 7$

Factor $5$ out of $35$ .

$f (\frac{5 x + 35}{6}) = \frac{6}{5} \cdot \frac{5 x + 5 \cdot 7}{6} - 7$

Factor $5$ out of $5 x + 5 \cdot 7$ .

$f (\frac{5 x + 35}{6}) = \frac{6}{5} \cdot \frac{5 (x + 7)}{6} - 7$

Cancel the common factor of $6$ .

Cancel the common factor.

$f (\frac{5 x + 35}{6}) = \frac{6}{5} \cdot \frac{5 (x + 7)}{6} - 7$

Rewrite the expression.

$f (\frac{5 x + 35}{6}) = \frac{1}{5} \cdot (5 (x + 7)) - 7$

Cancel the common factor of $5$ .

Cancel the common factor.

$f (\frac{5 x + 35}{6}) = \frac{1}{5} \cdot (5 (x + 7)) - 7$

Rewrite the expression.

$f (\frac{5 x + 35}{6}) = x + 7 - 7$

Step 4

Combine the opposite terms in $x + 7 - 7$ .

Subtract $7$ from $7$ .

$f (\frac{5 x + 35}{6}) = x + 0$

Add $x$ and $0$ .

$f (\frac{5 x + 35}{6}) = x$