find the given fuctions f and g, find f*g and state the domain of f*g, f(x)=�ã2x-5,g(x)=|x-1|
To find the product of two functions, f and g, you need to calculate f*g, which is the product of the two functions.
First, let's find f*g:
f(x) = 2x - 5
g(x) = |x - 1|
f*g(x) = f(x) * g(x)
Replace f(x) with 2x - 5 and g(x) with |x - 1|:
f*g(x) = (2x - 5) * |x - 1|
Now, let's state the domain of f*g. The domain refers to all possible values of x for which the function is defined.
For f*g(x) = (2x - 5) * |x - 1|, we need to consider the domain restrictions of both f(x) = 2x - 5 and g(x) = |x - 1|.
The domain of f(x) = 2x - 5 is all real numbers because there are no restrictions on x.
The domain of g(x) = |x - 1| is also all real numbers, as the absolute value function is defined for all real numbers.
Therefore, the domain of f*g(x) is all real numbers.
To summarize:
f*g(x) = (2x - 5) * |x - 1|
Domain of f*g: All real numbers