Find f(g(x)) f(x)=6x-3 , g(x)=5/(x+3)

$f (x) = 6 x - 3$ , $g (x) = \frac{5}{x + 3}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{5}{x + 3})$ by substituting in the value of $g$ into $f$ .

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

Step 3

Multiply $6 (\frac{5}{x + 3})$ .

Combine $6$ and $\frac{5}{x + 3}$ .

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

Multiply $6$ by $5$ .

$f (\frac{5}{x + 3}) = \frac{30}{x + 3} - 3$

Step 4

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{x + 3}{x + 3}$ .

$f (\frac{5}{x + 3}) = \frac{30}{x + 3} - 3 \cdot \frac{x + 3}{x + 3}$

Step 5

Simplify terms.

Combine $- 3$ and $\frac{x + 3}{x + 3}$ .

$f (\frac{5}{x + 3}) = \frac{30}{x + 3} + \frac{- 3 (x + 3)}{x + 3}$

Combine the numerators over the common denominator.

$f (\frac{5}{x + 3}) = \frac{30 - 3 (x + 3)}{x + 3}$

Step 6

Simplify the numerator.

Factor $3$ out of $30 - 3 (x + 3)$ .

Factor $3$ out of $30$ .

$f (\frac{5}{x + 3}) = \frac{3 (10) - 3 (x + 3)}{x + 3}$

Factor $3$ out of $- 3 (x + 3)$ .

$f (\frac{5}{x + 3}) = \frac{3 (10) + 3 (- (x + 3))}{x + 3}$

Factor $3$ out of $3 (10) + 3 (- (x + 3))$ .

$f (\frac{5}{x + 3}) = \frac{3 (10 - (x + 3))}{x + 3}$

Apply the distributive property.

$f (\frac{5}{x + 3}) = \frac{3 (10 - x - 1 \cdot 3)}{x + 3}$

Multiply $- 1$ by $3$ .

$f (\frac{5}{x + 3}) = \frac{3 (10 - x - 3)}{x + 3}$

Subtract $3$ from $10$ .

$f (\frac{5}{x + 3}) = \frac{3 (- x + 7)}{x + 3}$

Step 7

Simplify with factoring out.

Factor $- 1$ out of $- x$ .

$f (\frac{5}{x + 3}) = \frac{3 (- (x) + 7)}{x + 3}$

Rewrite $7$ as $- 1 (- 7)$ .

$f (\frac{5}{x + 3}) = \frac{3 (- (x) - 1 \cdot - 7)}{x + 3}$

Factor $- 1$ out of $- (x) - 1 (- 7)$ .

$f (\frac{5}{x + 3}) = \frac{3 (- (x - 7))}{x + 3}$

Simplify the expression.

Rewrite $- (x - 7)$ as $- 1 (x - 7)$ .

$f (\frac{5}{x + 3}) = \frac{3 (- 1 (x - 7))}{x + 3}$

Move the negative in front of the fraction.

$f (\frac{5}{x + 3}) = - \frac{3 (x - 7)}{x + 3}$

Find f(g(x)) f(x)=6x-3 , g(x)=5/(x+3)

Related Questions

Support LCMGCF.com by disabling your adblocker.