For the function g(x)=14/x+3, find (g^-1o g)(4)
by definition, (g^-1 o g)(x) = x,
so, 4.
Connexus Inverse Relations and Functions
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thank you but how do you solve
To find the composition (g^-1o g)(4) for the function g(x) = 14/x + 3, we need to follow these steps:
1. Find the inverse of g(x), denoted as g^-1(x). The inverse function reverses the input and output of the original function.
To find the inverse of g(x), swap the position of x and y in the equation g(x) = 14/x + 3:
x = 14/y + 3
Then, solve for y:
y = (x - 3)/14
Therefore, the inverse function is g^-1(x) = (x - 3)/14.
2. Substitute 4 into g(x).
Replace x in g(x) = 14/x + 3 with 4:
g(4) = 14/4 + 3
Simplifying further:
g(4) = 3.5 + 3
g(4) = 6.5
3. Apply the inverse function g^-1 to the result obtained in step 2.
To find (g^-1o g)(4), we substitute the value 6.5 into the inverse function g^-1(x):
g^-1(6.5) = (6.5 - 3)/14
Simplifying further:
g^-1(6.5) = 3.5/14
g^-1(6.5) = 0.25
Therefore, (g^-1o g)(4) = 0.25.