Answer:
[tex]f^{-1}(4)=3[/tex]
Step-by-step explanation:
Given : Expression [tex]f(x)=\frac{3x-1}{2}[/tex]
To find : The inverse of the expression ?
Solution :
Expression [tex]f(x)=\frac{3x-1}{2}[/tex]
Let, h(x)=y then [tex]y=\frac{3x-1}{2}[/tex]
For inverse we replace the value of x and y and find the value of y in terms of x.
Replace the value of x and y,
[tex]x=\frac{3y-1}{2}[/tex]
Cross multiply,
[tex]2x=3y-1[/tex]
Adding 1 both side,
[tex]2x+1=3y[/tex]
Dividing by 3 both side,
[tex]\frac{2x+1}{3}=y[/tex]
The inverse of the f(x) is [tex]f^{-1}(x)=\frac{2x+1}{3}[/tex]
Put x=4,
[tex]f^{-1}(4)=\frac{2(4)+1}{3}[/tex]
[tex]f^{-1}(4)=\frac{8+1}{3}[/tex]
[tex]f^{-1}(4)=\frac{9}{3}[/tex]
[tex]f^{-1}(4)=3[/tex]
Therefore, [tex]f^{-1}(4)=3[/tex]
