The first pair of functions and the second pair of functions they both are inverse of each other
To determine if two functions are inverse, we need to check if the composition of the functions results in the identity function.
In other words, if we plug in one function into the other and simplify, we should get back the original input.
Let's apply this concept to the given functions
f(x) = 3x - 8 and g(x) = 1/3x + 8/32
To check if they are inverse, we'll substitute g(x) into f(x) and simplify:
f(g(x)) = f(1/3x + 8/32)
f(g(x)) = 3(1/3x + 8/32) - 8
f(g(x)) = x + 8/32 - 8
f(g(x)) = x - 7.75
Since f(g(x)) = x, these functions are inverses.
f(x) =
- 3 and g(x) = √(x + 3/2) for x ≥ 0
Let's substitute g(x) into f(x) and simplify:
f(g(x)) = f(√(x + 3/2)) = 2(√(x + 3/2))^2 - 3 = 2(x + 3/2) - 3 = 2x + 3 - 3 = 2x
Since f(g(x)) = x, these functions are inverse
The probable question may be:
Determine if the two function are inverse
1. f(x)=3x-8 ang g(x)=1/3x+8/3
2. f(x)=2x^2-3 and g(x)=\sqrt{x+3/2} for x>=0