Explore: Evaluating Combinations of Functions Solutions

Evaluating Combinations of Functions Solutions

The value of a combination of functions is determined when the value of x is given. 
Substitute the x-value into all of the functions and simplify .

Example 5

Evaluate.

$f (x) = 3 x^{2} - x - 1 g (x) = 2 x + 1 h (x) = \frac{1}{x - 2}$

$(f h) (0)$

$(f h) (0) = f (0) \cdot h (0) (f h) (0) = (3 {(0)}^{2} - (0) - 1) (\frac{1}{0 - 2}) (f h) (0) = (- 1) (- \frac{1}{2}) (f h) (0) = \frac{1}{2}$

$(\frac{g h}{f}) (- 1)$

$(\frac{g h}{f}) (- 1) = \frac{g (- 1) \cdot h (- 1)}{f (- 1)} (\frac{g h}{f}) (- 1) = \frac{2 (- 1) + 1}{3 {(- 1)}^{2} - (- 1) - 1} \cdot \frac{1}{- 1 - 2} (\frac{g h}{f}) (- 1) = - \frac{1}{3} \cdot - \frac{1}{3} (\frac{g h}{f}) (- 1) = \frac{1}{9}$

Example 6

Evaluate.

$(f + g) (- 2) (f + g) (- 2) = f (- 2) + g (- 2)$

$(f + g) (- 2) = 3 + 0.5 (f + g) (- 2) = 3.5$

$(g - f) (0)$

$(g - f) (0) = g (0) - f (0) (g - f) (0) = 1.5 - (- 1) (g - f) (0) = 2.5$

$(f g) (1.5)$

$(f g) (1.5) = f (1.5) \cdot g (1.5) (f g) (1.5) = (0) (0.5) (f g) (1.5) = 0$

$(\frac{g}{f}) (0.5)$

$(\frac{g}{f}) (0.5) = \frac{g (0.5)}{f (0.5)} (\frac{g}{f}) (0.5) = \frac{0.5}{- 2} (\frac{g}{f}) (0.5) = - 0.25$