Find g(f(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.

$g (f (x))$

Step 2

Evaluate $g (\frac{6}{5} x - 7)$ by substituting in the value of $f$ into $g$ .

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

Step 3

Simplify the numerator.

Factor $5$ out of $5 (\frac{6}{5} x - 7) + 35$ .

Factor $5$ out of $35$ .

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

Factor $5$ out of $5 (\frac{6}{5} x - 7) + 5 \cdot 7$ .

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

Combine $\frac{6}{5}$ and $x$ .

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

Add $- 7$ and $7$ .

$g (\frac{6}{5} x - 7) = \frac{5 (\frac{6 x}{5} + 0)}{6}$

Add $\frac{6 x}{5}$ and $0$ .

$g (\frac{6}{5} x - 7) = \frac{5 (\frac{6 x}{5})}{6}$

Step 4

Combine $5$ and $\frac{6 x}{5}$ .

$g (\frac{6}{5} x - 7) = \frac{\frac{5 (6 x)}{5}}{6}$

Step 5

Multiply $5$ by $6$ .

$g (\frac{6}{5} x - 7) = \frac{\frac{30 x}{5}}{6}$

Step 6

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{30 x}{5}$ by cancelling the common factors.

Factor $5$ out of $30 x$ .

$g (\frac{6}{5} x - 7) = \frac{\frac{5 (6 x)}{5}}{6}$

Factor $5$ out of $5$ .

$g (\frac{6}{5} x - 7) = \frac{\frac{5 (6 x)}{5 (1)}}{6}$

Cancel the common factor.

$g (\frac{6}{5} x - 7) = \frac{\frac{5 (6 x)}{5 \cdot 1}}{6}$

Rewrite the expression.

$g (\frac{6}{5} x - 7) = \frac{\frac{6 x}{1}}{6}$

Divide $6 x$ by $1$ .

$g (\frac{6}{5} x - 7) = \frac{6 x}{6}$

Step 7

Cancel the common factor of $6$ .

Cancel the common factor.

$g (\frac{6}{5} x - 7) = \frac{6 x}{6}$

Divide $x$ by $1$ .

$g (\frac{6}{5} x - 7) = x$