Find (f/g)(4) and (f+g)(4)?

If f(x)=x^2+2x-3 and g(x)=x^2-9, Find (f/g)(4) and (f+g)(4)

Jun 21, 2018

$\left(\frac{f}{g}\right) \left(4\right) = \frac{f \left(4\right)}{g \left(4\right)} = \frac{21}{7} = 3$
$\left(f + g\right) \left(4\right) = f \left(4\right) + g \left(4\right) = 21 + 7 = 28$

Explanation:

The notation $\left(\frac{f}{g}\right) \left(x\right)$ is just a way to say $\frac{f \left(x\right)}{g \left(x\right)}$ and
$\left(f + g\right) \left(x\right)$ is another way to say $f \left(x\right) + g \left(x\right)$
$\left(f g\right) \left(x\right)$ is another way to say $f \left(x\right) \cdot g \left(x\right)$

Jun 21, 2018

$\left(\frac{f}{g}\right) \left(4\right) = 3$, $\left(f + g\right) \left(4\right) = 28$

Explanation:

$f \left(x\right) = {x}^{2} + 2 x - 3$ , $g \left(x\right) = {x}^{2} - 9$
$f \left(4\right) = {4}^{2} + 2 \cdot 4 - 3 = 16 + 8 - 3 = 21$
$g \left(4\right) = {4}^{2} - 9 = 16 - 9 = 7$

$\left(\frac{f}{g}\right) \left(4\right) = f \frac{4}{g} \left(4\right)$

$\left(\frac{f}{g}\right) \left(4\right) = \frac{21}{7} = 3$

$\left(f + g\right) \left(4\right) = f \left(4\right) + g \left(4\right)$

$\left(f + g\right) \left(4\right) = 21 + 7 = 28$