Question

Suppose that the functions and are defined as follows.

Answer 1

Answer: (q°r)(4) = 30

(r°q)(4) = 36

Explanation:

First, when we have two functions f(x) and g(x), we have that:

(g°f)(x) = g(f(x))

So we are actually evaluating one function with other function.

Now, solving the problem:

q(x) = 2x - 2

r(x) = x^2

we have:

(q°r)(x) = q(r(x)) = 2*r(x) - 2 = 2*(x^2) - 2

(r°q)(x) = r(q(x)) = q(x)^2 = (2*x - 2)^2

Then:

(q°r)(4) = q(r(4)) = 2*r(4) - 2 = 2*(4^2) - 2 = 2*16 - 2 = 32 - 2 = 30.

(r°q)(4) = r(q(4)) = q(4)^2 = (2*4 - 2)^2 = 6^2 = 36.