Question

Verify that f(x) and g(x) are inverse functions: a). f(x)=5 x+2, g(x)=x-2/5

Answer 1

To verify whether f(x) = 5x+2 and g(x) = (x-2)/5 are inverse functions, we need to compose them and check if we get the identity function. By composing f(g(x)) and g(f(x)), we find that both equal x, confirming that f(x) and g(x) are indeed inverse functions.

Step-by-step explanation:

To verify that f(x) = 5x+2 and g(x) = (x-2)/5 are inverse functions, we need to show that when we compose them, we get the identity function. In other words, f(g(x)) = x and g(f(x)) = x for all x in their domains.

To start, let's find f(g(x)):

f(g(x)) = 5(g(x)) + 2
= 5((x-2)/5) + 2
= 5(x-2)/5 + 2
= x - 2 + 2
= x

Since f(g(x)) = x, we have shown that g(x) is the inverse function of f(x).

Next, let's find g(f(x)):

g(f(x)) = (f(x) - 2)/5
= (5x+2 - 2)/5
= 5x/5
= x

Again, we have shown that g(f(x)) = x, confirming that f(x) and g(x) are inverse functions.