Find f(g(x)) f(x)=7/(x-8) , g(x)=7/x+8

$f (x) = \frac{7}{x - 8}$ , $g (x) = \frac{7}{x} + 8$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{7}{x} + 8)$ by substituting in the value of $g$ into $f$ .

$f (\frac{7}{x} + 8) = \frac{7}{(\frac{7}{x} + 8) - 8}$

Step 3

Simplify the denominator.

Subtract $8$ from $8$ .

$f (\frac{7}{x} + 8) = \frac{7}{\frac{7}{x} + 0}$

Add $\frac{7}{x}$ and $0$ .

$f (\frac{7}{x} + 8) = \frac{7}{\frac{7}{x}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{7}{x} + 8) = 7 (\frac{x}{7})$

Step 5

Cancel the common factor of $7$ .

Cancel the common factor.

$f (\frac{7}{x} + 8) = 7 (\frac{x}{7})$

Rewrite the expression.

$f (\frac{7}{x} + 8) = x$