I need to find the rule of the inverse of the function f(x) = 6x + 4.
Should I factorize is to x/6 - 2/3 or should I leave it as (x - 4)/6.
Thanks
your welcome
makes no difference. They are the same.
To find the rule of the inverse of a given function, you need to interchange the variables x and y and solve for y.
Let's start by interchanging the variables in the function f(x) = 6x + 4 to x = 6y + 4.
Now, let's solve for y:
x = 6y + 4
To isolate y, we can start by subtracting 4 from both sides:
x - 4 = 6y
Next, divide both sides by 6 to solve for y:
(x - 4) / 6 = y
So, the rule of the inverse function is y = (x - 4) / 6.
Regarding your question about leaving it as (x - 4) / 6 or factoring it to x/6 - 2/3, both are correct representations of the inverse function. It is just two different forms of expressing the same solution.
If you prefer the factored form, you can write it as:
y = x/6 - 2/3
And if you prefer the simplified form, you can write it as:
y = (x - 4) / 6
Both expressions represent the inverse function of f(x) = 6x + 4.