If f(x)=x^2-2 and g(x)=1/(3x) (x does not equal 0), find (fxg)(-2)
Given:
f(x)=x²-2
g(x)=1/(3x)
I assume you are working with composite functions, and you are looking for
(f∘g)(x)
=f(g(x))
=f(1/(3x))
=(1/3x)²-2
=1/(9x²)-2
(f∘g)(2)
=1/(9*2²)-2
=1/(9*2²)-2
=1/36-2
=-71/36
To find the value of (f * g)(-2), we need to evaluate the composition of f(x) and g(x) at x = -2.
First, let's find the value of f(x) when x = -2:
f(x) = x^2 - 2
f(-2) = (-2)^2 - 2
f(-2) = 4 - 2
f(-2) = 2
Next, let's find the value of g(x) when x = -2:
g(x) = 1 / (3x)
g(-2) = 1 / (3 * -2)
g(-2) = 1 / (-6)
g(-2) = -1/6
Now, let's multiply f(-2) and g(-2) together to find (f * g)(-2):
(f * g)(-2) = f(-2) * g(-2)
(f * g)(-2) = 2 * (-1/6)
(f * g)(-2) = -2/6
(f * g)(-2) = -1/3
Therefore, (f * g)(-2) = -1/3.