what is g(f(x))? and f(g(x))?
if f(x)=(1)/(sqaure root3x) and
g(x)=x^2-5
Thanks!
f(x) = x - 1
g(x) = x + 1
f(g(x)) = g(x) - 1 = x + 1 - 1 = x
g(f(x)) = f(x) + 1 = x - 1 + 1 = x
To find g(f(x)), we first need to substitute f(x) into the function g(x).
Given f(x) = 1/√(3x) and g(x) = x^2 - 5, we can write g(f(x)) as:
g(f(x)) = g(1/√(3x))
Now substitute f(x) = 1/√(3x) into g(x):
g(f(x)) = (1/√(3x))^2 - 5
Simplifying further:
g(f(x)) = 1/(3x) - 5
So g(f(x)) = 1/(3x) - 5.
Now, let's find f(g(x)). We substitute g(x) into the function f(x):
Given f(x) = 1/√(3x) and g(x) = x^2 - 5, we can write f(g(x)) as:
f(g(x)) = f(x^2 - 5)
Substituting g(x) = x^2 - 5 into f(x):
f(g(x)) = 1/√(3(x^2 - 5))
That's the expression for f(g(x)).