Question

If f(x) = 3x 2 and g(x) = x2 1, which expression is equivalent to (f circle g) (x)?.

Answer 1

This can be solved by substituting the output of function g in function f.

The expression that is equivalent to $(f\circ g)(x)$ is $3x^2 + 5$

What are function of functions and how are they represented?

Function of function, as the name suggests, are functions applied over functions themselves. This is also called function composition.

We have input. We apply one function on that input. Then we apply another function on the output obtained by the first function. This whole function application on first input is called function of functions. The resultant function which maps the input x to the final output is called function of function.

If first function is g( and the other function is f, then we can write the resultant function of function as  $(f\circ g)(x)$ where the x is the input to first function.

Thus, we have;

$(f\circ g)(x) = f(g(x))$

How to get the expression for  $(f\circ g)(x)$ by knowing what f(x) and g(x) are?

We will put whatever g(x) outputs as input to f.

Thus,

$g(x) = x^2 + 1\\\\ f(x) = 3x + 2\\\\ (f\circ g)(x) = f(g(x)) = 3(g(x)) + 2 = 3( (x^2 + 1) ) + 2 = 3x^2 + 3 + 2 = 3x^2 + 5\\\\ (f \circ g)(x) = 3x^2 + 5$

Thus, the expression that is equivalent to $(f\circ g)(x)$ is $3x^2 + 5$

Learn more about function composition here:

https://brainly.com/question/17299449