Question

Consider $f:R\to R$ given by $f\left(x\right)=4x+3$. Show that $f$ is invertible. Find the inverse of $f$

• A. $y=\frac{(x+3)}{4}$
• B. $y=\frac{(x-3)}{4}$
• C. $y=\frac{(-x-3)}{4}$
• D. $y=\frac{(x-3)}{-4}$

Answer 1

The correct option is B $y=\frac{(x-3)}{4}$

A function is a one-to-one function if and only if each second element corresponds to one and only one first element. (each x and y value is used only once)
Use the horizontal line test to determine if a function is a one-to-one function.
If ANY horizontal line intersects your original function in ONLY ONE location, your function will be a one-to-one function and its inverse will also be a function.
Now,
$f\left(x\right)=4x+3$ is one-to-one function , Therefore it has inverse function
Now express the given function in following way
$x=4y+3$ , Now express y in terms of x, y will be inverse
$y=\frac{(x-3)}{4}$ is $f^{-1}$