# How do you find (f-g)(3) given f(x)=x^2-1 and g(x)=2x-3 and h(x)=1-4x?

##### 1 Answer
Apr 3, 2017

Compute $\left(f - g\right) \left(x\right)$ and then evaluate at $x = 3$

OR

Evaluate $f \left(3\right) \text{ and } g \left(3\right)$ and then perform the subtraction.

$\left(f - g\right) \left(3\right) = f \left(3\right) - g \left(3\right)$

#### Explanation:

Compute $\left(f - g\right) \left(x\right)$:

$\left(f - g\right) \left(x\right) = f \left(x\right) - g \left(x\right)$

Substitute the equivalents for $f \left(x\right) \text{ and } g \left(x\right)$

$\left(f - g\right) \left(x\right) = {x}^{2} - 1 - \left(2 x - 3\right)$

Distribute the minus sign:

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

Combine like terms:

$\left(f - g\right) \left(x\right) = {x}^{2} - 2 x + 2$

Evaluate at $x = 3$:

$\left(f - g\right) \left(3\right) = {3}^{2} - 2 \left(3\right) + 2$

$\left(f - g\right) \left(3\right) = 5$

OR

Evaluate $f \left(x\right) \text{ at } x = 3$:

$f \left(3\right) =$3^2 - 1

$f \left(3\right) = 8$

Evaluate $g \left(x\right) \text{ at } x = 3$

$g \left(3\right) = 2 \left(3\right) - 3$

$g \left(3\right) = 3$

$\left(f - g\right) \left(3\right) = f \left(3\right) - g \left(3\right)$

$\left(f - g\right) \left(3\right) = 8 - 3$

$\left(f - g\right) \left(3\right) = 5$

Either always works.