Question

Given f(x)=4x²−11 and g(x)=4x²−11, find h(x) such that f(x)=(1°g)(x).

Answer 1

To find h(x) such that f(x)=(1°g)(x), we need to compose the functions f(x) and g(x).

Step-by-step explanation:

To find h(x) such that f(x)=(1°g)(x), we need to compose the functions f(x) and g(x). The composition of two functions f and g is written as (f ° g)(x) and is defined as f(g(x)).

So, in this case, (1°g)(x) = f(g(x)). Given that f(x) = 4x²−11 and g(x) = 4x²−11, we can substitute g(x) into f(x) to get (1°g)(x) = f(g(x)) = f(4x²−11).

We can now simplify this expression to get the final equation for h(x).

Let's substitute g(x) = 4x²−11 into f(x) = 4x²−11:
h(x) = f(g(x)) = f(4x²−11).