tis a little bit confusing if i say so myself.

Question

g(x) = -5/x-8

f(x) = 2^x

h(x) = (g • f)(x)

The domain of h(x) can be shown as x ≠ k.

What is the value of k??

Answer 1

Hey Jim, thanks for the question!

Firstly, I'm not sure whether the -8 in your g(x) is in the denominator of the equation or not, so whether the equation is (-5/x) - 8 OR -5/(x-8).

I'm going to walk through the steps of solving this problem using g(x) = -5/(x-8), but don't forget to include parenthesis in the future in ambiguous cases like this one!

The first step in this problem is to write out exactly what h(x) is, so begin by multiplying g(x) and f(x).

The equation you end up with is h(x) = ((-5)(2^x))/(x-8)

Now that we have this equation for h(x), we only need to ask ourselves when a value is excluded from the domain. A common instance of one value not being a part of the domain is when the denominator of a fraction is equal to zero. You might have heard the following: "anything divided by 0 is undefined."

In our equation for h(x), the denominator is x - 8. For what value of x is the denominator equal to zero? At x = 8! So, the domain of h(x) can be shown as x ≠ 8.