SOLUTION: find (f-g)(x). What is the domain of f/g f(x)=2x-5 g(x)=2-x

Question 147184: find (f-g)(x). What is the domain of f/g
f(x)=2x-5 g(x)=2-x
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given property

Plug in and

Distribute.

Combine like terms

Start with the given property

Plug in and

Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.

Subtract 2 from both sides

Combine like terms on the right side

Divide both sides by -1 to isolate x

Divide

Since makes the denominator equal to zero, this means we must exclude from our domain

So our domain is:

which in plain English reads: x is the set of all real numbers except

So our domain looks like this in interval notation

note: remember, the parenthesis excludes 2 from the domain

If we wanted to graph the domain on a number line, we would get:

Graph of the domain in blue and the excluded value represented by open circle

Notice we have a continuous line until we get to the hole at (which is represented by the open circle).
This graphically represents our domain in which x can be any number except x cannot equal 2

RELATED QUESTIONS
Find (fg)(x). What is the domain of f/g f(x)=2x-5,... (answered by nerdybill)

3.14 Given f(x)=x-4 and g(x)=4x^2, find f+g, f-g, fg, and f/g. Determine the domain... (answered by ikleyn)

3.14 Given that f(x)=2x+7 and g(x)=5x^2, find f+g, f-g, fg, and f/g. Determine the... (answered by nerdybill)

find the following a) (f+g)(x) b) (f-g)(x) c)(fg)(x)d)(f/g)(x) what is the domain of... (answered by solver91311)

given that f(x)=x^2 and g(x)=sqr rt 5-x, find the following. a)f/g b)what is the domain (answered by MathLover1)

========================================================================================== (answered by MathLover1)

3.21 Find f+g, f-g and f/g. Determine the domain for each function. f(x)=4x+8,... (answered by fractalier)

for f(x)= x^2-64 and g(x)= 2x+3, what is the domain of... (answered by Fombitz)

f(x) = x x+2 , g(x) = x x−1 Find the domain of f... (answered by josgarithmetic)