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

Question 147183: Find (fg)(x). What is the domain of f/g
f(x)=2x-5, g(x)=2-x
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Find (fg)(x). What is the domain of f/g
f(x)=2x-5, g(x)=2-x
.
Domain is the "range" of values that 'x' can take for the expression.
.
Your "expression" is f/g or substituting in the values for f and g we get:
(2x-5)/(2-x)
Looking at the above, the only values that would make the expression "undefined" is when the denominator goes to zero. (remember, anything over 0 is undefined).
.
Therefore, to find that value of x that we cannot use for the expression, set 2-x to zero and solve for x:
2-x = 0
2 = x
.
Therefore, the domain is:
All real numbers EXCEPT 2.

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