Two functions f and g are defined by
f:x = 25 /(3x-2)
g:x = x^2
Find the composite function
Please show all calculations, thank you!
To find the composite function, we need to evaluate g(f(x)). This means we will take the function f(x) as the input for the function g(x).
Let's start by substituting f(x) into g(x):
g(f(x)) = g(25 /(3x-2))
Now, let's substitute x = 25 /(3x-2) into g(x) (which is x^2):
g(f(x)) = (25 /(3x-2))^2
To simplify this expression, we square the numerator and denominator:
g(f(x)) = (25^2) / (3x-2)^2
Thus, the composite function g(f(x)) is expressed as (25^2) / (3x-2)^2.