Answer:
or
Step-by-step explanation:
Given
Required
Write a rule for g(x)
See attachment for grid
From the attachment, we have:
We can represent g(x) as:
So, we have:
For:
This gives:
Solve for n
To confirm this value of n, we make use of:
So, we have:
This gives:
Solve for n
Hence:
or:
1) Inverse function:
2)
3)
Step-by-step explanation:
1)
In this first method, we want to find the inverse function of .
The original function is:
We rewrite it as
We swap the name of the variables:
Adding +4 on both sides:
And dividing by 3 on both sides:
which is identical to :
2)
In this second method, we want to use the output of one function as input to the other function, and show that the output value is equal to the imput value.
We start using the function
We choose . We find:
Now we use this output value as input in the function
Substituting ,
So, the final output value (1) is equal to the input value (1).
3)
Here we want to verify that the two are inverse functions by showing that
We have
Substituting g(x) into f(x),
Viceversa, we want to show that
Substituting g(x) into f(x), we get
So, the two functions are one the inverse of the other.
Learn more about inverse functions:
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