Question

If mc018-1.jpg and g(x) = 5x – 4, what is the domain of mc018-2.jpg?

Answer 1

First, we work out the composite function fg(x)

$fg(x)= \frac{(5x-4)-3}{5x-4} = \frac{5x-7}{5x-4}$

We need to check the expression of the denominator for the value of x that would make $5x-4=0$.

$5x-4=0$
$x= \frac{4}{5}$

We cannot have $x= \frac{4}{5}$ because we cannot have zero value for denominator

The value for x in fg(x) can be any number apart from $x= \frac{4}{5}$

Correct answer: third option {x | x≠4/5}

Answer 2

Answer:

The domain of the function (f*g)(x) = {x|x≠4/5} Option C.

Step-by-step explanation:

First, you need to combine the functions f(x) and g(x) into the new function equation (f*g)(x). This looks complicated, but the first pair of parenthesis make it confusing. Let's say the end result of f times g is h. The new function would look like this: h(x).

So h(x) = (x-3/x)(5x-4)

Now use the FOIL method to multiply each binomial and cancel out the parenthesis.

FOIL

First

Outside

Inside

Last

For your last step, simplify your answer and set x off to one side. You are done!

If your answer comes out in decimal form, as it was 0.8 in this equation, convert it into fraction form. If it is not a terminating decimal, round it UP not down to make it a fraction. Hope this helps!