for the given functions f and g find f*g. f(x) = sqrt x -3
g(x) = x^2 -7x + 9
Help Please!
f*g(x) = sqrt(x^2-7x+9) + 1
That cannot be further simplified.
but how did you get it? and I'm suppose to state domain too?
To find the product of the functions f and g, denoted as f * g, we need to multiply the two functions together.
Given:
f(x) = √x - 3
g(x) = x^2 - 7x + 9
To find f * g, we substitute g(x) into f(x) wherever we see x.
f(x) * g(x) = (√x - 3) * (x^2 - 7x + 9)
To simplify, we can distribute (multiply) each term in the first function by each term in the second function:
f * g = (√x * x^2) + (√x * -7x) + (√x * 9) + (-3 * x^2) + (-3 * -7x) + (-3 * 9)
Now, let's multiply each of these terms:
f * g = x^(5/2) - 7x^(3/2) + 9√x - 3x^2 + 21x - 27
Therefore, the product of the functions f and g is:
f * g = x^(5/2) - 7x^(3/2) + 9√x - 3x^2 + 21x - 27