Question

Select the equation that is the inverse of the given function f(x)=x-3/5

Answer 1

$f(x)=\dfrac{x-3}{5}\to y=\dfrac{x-3}{5}\\\\\text{Interchange the y and the x}\\\\x=\dfrac{y-3}{5}\\\\\text{Solve for y}\\\\\dfrac{y-3}{5}=x\qquad|\cdot5\\\\y-3=5x\qquad|+3\\\\y=5x+3\\\\Answer:\ B.\ f^{-1}(x)=5x+3$

Answer 2

Answer:

(B) $f^{-1}(x)=5x+3$

Step-by-step explanation:

Given: The function $f(x)=\frac{x-3}{5}$.

To find: The inverse of the given function $f(x)=\frac{x-3}{5}$.

Solution: Let us consider the function $f(x)=\frac{x-3}{5}$, Let f(x)=y, then the function becomes

$y=\frac{x-3}{5}$

Now, interchanging the variables as interchange y with x and x with y, we get

$x=\frac{y-3}{5}$

Now, solving for y, we have

$y=5x+3$

Thus, the inverse can be written as:

$f^{-1}(x)=5x+3$

Hence, option (B) is correct.