Given f(x) = 2x − 1 and g(x) = 4x − 4, evaluate the composite function.
g[f(x)]
same method as the two posts above this
To evaluate the composite function g[f(x)], we need to substitute the function f(x) into the function g(x).
First, let's find the value of f(x) by substituting x into the expression for f(x):
f(x) = 2x - 1.
Now, we can substitute f(x) into the expression for g(x):
g[f(x)] = g[2x - 1].
To find g[f(x)], we replace x in the expression for g(x) with the expression for f(x):
g[f(x)] = 4(2x - 1) - 4.
Now, simplify the expression by performing the operations within the parentheses and then applying the multiplication and subtraction:
g[f(x)] = 8x - 4 - 4.
Finally, combine like terms to get the result:
g[f(x)] = 8x - 8.
So, the value of the composite function g[f(x)] is 8x - 8.