Answer:
\(f^{-1}(4)=3\)
Step-by-step explanation:
Given : Expression \(f(x)=\frac{3x-1}{2}\)
To find : The inverse of the expression ?
Solution :
Expression \(f(x)=\frac{3x-1}{2}\)
Let, h(x)=y then \(y=\frac{3x-1}{2}\)
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,
\(x=\frac{3y-1}{2}\)
Cross multiply,
\(2x=3y-1\)
Adding 1 both side,
\(2x+1=3y\)
Dividing by 3 both side,
\(\frac{2x+1}{3}=y\)
The inverse of the f(x) is \(f^{-1}(x)=\frac{2x+1}{3}\)
Put x=4,
\(f^{-1}(4)=\frac{2(4)+1}{3}\)
\(f^{-1}(4)=\frac{8+1}{3}\)
\(f^{-1}(4)=\frac{9}{3}\)
\(f^{-1}(4)=3\)
Therefore, \(f^{-1}(4)=3\)