f(x)2x^(2)+x-3 g(x)=x-1
Perform the indicated operation, then find the domain (f*g)(x)
To find the product of two functions, f(x) and g(x), we need to multiply them:
(f * g)(x) = f(x) * g(x)
In this case, f(x) = 2x^2 + x - 3 and g(x) = x - 1:
(f * g)(x) = (2x^2 + x - 3) * (x - 1)
To compute the product, we'll use the distributive property:
(f * g)(x) = 2x^2 * (x - 1) + x * (x - 1) - 3 * (x - 1)
Now, let's simplify each term:
(f * g)(x) = 2x^3 - 2x^2 + x^2 - x - 3x + 3
Combine like terms:
(f * g)(x) = 2x^3 - x^2 - 4x + 3
So, the product of f(x) and g(x) is 2x^3 - x^2 - 4x + 3.
Now, let's find the domain of (f * g)(x). The domain is the set of all possible x-values for which the function is defined.
In this case, since polynomial functions are defined for all real numbers, the domain of (f * g)(x) is all real numbers.
Therefore, the domain of (f * g)(x) is (-∞, ∞).
To perform the indicated operation, we need to find the product of the functions f(x) and g(x). This can be done by multiplying each term of f(x) by each term of g(x) and then simplifying.
f(x) = 2x^(2) + x - 3
g(x) = x - 1
To find (f*g)(x), multiply each term of f(x) by each term of g(x):
(f*g)(x) = (2x^(2) + x - 3)(x - 1)
We can solve this by using the distributive property and combining like terms:
(f*g)(x) = 2x^(3) + x^(2) - 3x - 2x^(2) - x + 3
Now, simplify the expression by combining like terms:
(f*g)(x) = 2x^(3) - x^(2) - 4x + 3
To find the domain of the function (f*g)(x), we need to consider any potential domain restrictions. In this case, because we have polynomials, there are no restrictions on the domain. Therefore, the domain of the function is all real numbers (-∞, +∞).
If you mean f(x) = 2x^2+x-3 then
f(g) = 2g^2+g-3
= 2(x-1)^2+(x-1)-3
= 2x^2-3x-2