The inverse of the function will be y = x/2 + 3/2. Yes, inverse is a function as well.
Functions that "undo" one another are known as inverse functions. In other words, f(g(x)) = g(f(x)) = x if g(x) is the inverse of f(x). We have a great approach we can use to achieve this given an equation for which we wish to get the inverse.
Not all functions have their opposite. It is simple to see that f(x) will never take on the same value again if f(x) has an inverse. We give this asset a unique name.
If each member of the range corresponds to precisely one element of the domain, a function is said to be one-to-one (f(x)).
Given,
We have a function,
y=2 x-3
Add 3 to each side.
⇒ y + 3 = 2x
Divide by 2 and then either
⇒ x = y/2 + 3/2 or y/2 + 3/2
Just change the labels now, x to y.
⇒ y = x/2 + 3/2
So, the inverse of given function is y = x/2 + 3/2
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