Question

If f(x) = 3x - 5 and g(x) = x², calculate (f ∘ g)(3) and (g ∘ f)(3).

Answer 1

To calculate (f ∘ g)(3), we first find g(3) and then apply f resulting in 22. For (g ∘ f)(3), we calculate f(3) first and then apply g, leading to 16.

Step-by-step explanation:

To calculate (f \circ g)(3), we first need to compute g(3), which is 32, and then apply the function f to that result. To compute (g \circ f)(3), we first calculate f(3) and then apply the function g to that result

First, let's find (f \circ g)(3):

Compute g(3) = 32 = 9.

Apply f to the result: f(g(3)) = f(9) = 3 \cdot 9 - 5 = 27 - 5 = 22.

For (g \circ f)(3):

Compute f(3) = 3 \cdot 3 - 5 = 9 - 5 = 4.

Apply g to the result: g(f(3)) = g(4) = 42 = 16.

Therefore, the results are:

(f \circ g)(3) equals 22

(g \circ f)(3) equals 16