Question

How do I find (f•g)⁻¹ using f(x) = x + 2 and g(x) = 2x - 5?

A) (f•g)⁻¹(x) = 2x - 3
B) (f•g)⁻¹(x) = 2x - 7
C) (f•g)⁻¹(x) = 2x + 3
D) (f•g)⁻¹(x) = x - 7

Answer 1

To find (f•g)⁻, we need to find the inverse of the composition of f(x) = x + 2 and g(x) = 2x - 5. We can do this by swapping x and y and solving for y. The inverse of (f•g) is (f•g)⁻(x) = (x + 3)/2.

Step-by-step explanation:

To find (f•g)⁻ using f(x) = x + 2 and g(x) = 2x - 5, we need to find the inverse of the composition of f and g. Here are the steps:

1. Start with the composition of f and g: (f•g)(x) = f(g(x)) = f(2x - 5)
2. Replace x in the function f with (2x - 5): (f•g)(x) = (2x - 5) + 2 = 2x - 3
3. Now, to find the inverse, we need to swap x and y and solve for y: y = 2x - 3 ⇒ x = 2y - 3 ⇒ x + 3 = 2y ⇒ (x + 3)/2 = y
4. So, the inverse of (f•g) is (f•g)⁻(x) = (x + 3)/2