If f(x) = 4x² and g(x) = 5x, what is g(f(2x))?

Solution:

Given function f(x) = 4x² and g(x) = 5x

A function, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)

Here, we can replace x with 2x

f(2x) = 4(2x)² = 4(4x²) = 16x²

Now, to find the composite function, g(f(2x)), we need to put value of f(2x) in place of ‘x’ in g(x)

g(f(2x)) = g(16x²) = 5(16x²) = 80x²

Therefore, g(f(2x)) = 80x²

If f(x) = 4x² and g(x) = 5x, what is g(f(2x))?

Summary:

If f(x) = 4x² and g(x) = 5x, then g(f(2x)) = 80x²