Question

How do you find the inverse of `f(x) =1/(4x+7)` and is it a function?

Answer 1

If `y = f(x) = 1/(4x + 7), f^(-1)(y)=(1-7y)/(4y)=x` is a function.
In simple words, if y is a function of x, inversely, x is a function of y. .

Explanation:

If y = f(x), the inverse relation is `x=f^(-1)(y)`.

The mapping, either way, is `1-1, or many-1, or 1-many`

In f(x) = arc sin (x), it is 1-many mapping.

In f(x) = sin x, it is many-1 mapping.

Yet, by definition,

`f^(-!)(f(x)) = x and f( f^(-1)(y))=y`.

Here, solving for x, the inverse relation is `x = (1-7y)/(4y)`.
This is 1-1 mapping. .