Answer:
Option 2 - [tex]f^{-1}(x)[/tex] = The quantity of 4x plus 3, divided by 5.
Step-by-step explanation:
Given : f(x) = the quantity of 5x minus 3, divided by 4
To find : Which of the below expressions is correct?
Solution :
We can write the expression as
[tex]f(x)=\frac{5x-3}{4}[/tex]
Let, f(x)=y
[tex]y=\frac{5x-3}{4}[/tex]
To find inverse, interchange the place of x and y and solve for y.
[tex]x=\frac{5y-3}{4}[/tex]
[tex]4x=5y-3[/tex]
[tex]4x+3=5y[/tex]
[tex]\frac{4x+3}{5}=y[/tex]
So, The inverse of f(x) is [tex]f^{-1}(x)=\frac{4x+3}{5}[/tex]
or [tex]f^{-1}(x)[/tex] = The quantity of 4x plus 3, divided by 5.
Therefore, option 2 is correct.
