Question

For f(x)=2x−5​/9 and g(x)=9x+5​/2, verify that f and g are inverse functions.

Answer 1

To verify that f(x) and g(x) are inverse functions, we need to find the composition of f(g(x)) and g(f(x)). If both compositions result in the identity function, then f(x) and g(x) are inverses.

Step-by-step explanation:

In order to verify that f(x) and g(x) are inverse functions, we need to show that their compositions result in the identity function.

Let's first find the composition of f(g(x)):

f(g(x)) = f(9x + 5/2) = 2(9x + 5/2) - 5/9 = 18x + 10 - 5/9 = 18x + 9 5/9.

Now, let's find the composition of g(f(x)):

g(f(x)) = g(2x - 5/9) = 9(2x - 5/9) + 5/2 = 18x - 5 + 5/2 = 18x - 5 5/2.

Since f(g(x)) = x and g(f(x)) = x, we can conclude that f(x) and g(x) are inverse functions.