To perform the function operation $(f - g)(x)$, we subtract the function $g(x)$ from the function $f(x)$.

Given:

• $f(x) = x^2 - 1$
• $g(x) = 2x - 3$

Step-by-step process:

$(f - g)(x) = f(x) - g(x)$

Substitute the expressions for $f(x)$ and $g(x)$: $(f - g)(x) = (x^2 - 1) - (2x - 3)$

Distribute the negative sign: $(f - g)(x) = x^2 - 1 - 2x + 3$

Now combine like terms: $(f - g)(x) = x^2 - 2x + 2$

So, the result of $(f - g)(x)$ is: $(f - g)(x) = x^2 - 2x + 2$

Do you want any further details or have any questions?

Here are 5 related questions you could explore:

1. What is $(f + g)(x)$ using the same functions $f(x)$ and $g(x)$?
2. How would you find $(f \cdot g)(x)$, the product of the functions?
3. Can you determine the domain of $(f - g)(x)$?
4. What is $(g - h)(x)$ using $g(x)$ and $h(x)$?
5. How would you solve for $x$ if $(f - g)(x) = 0$?

Tip: Always simplify expressions by distributing negative signs and combining like terms carefully to avoid mistakes!