Answer:
\(f^{-1}(4)=3\)
Step-by-step explanation:
we need to find f(x) , which is stated as " the quantity of 3x minus 1, divided by 2"
the quantity of 3x minus 1 which means, 3x - 1
and then divided by 2 gives,
\(\frac{3x-1}{2}\)
so,
\(y=f(x)=\frac{3x-1}{2}\)
to find inverse of f(x) , we switch x and y,
\(x=\frac{3y-1}{2}\)
multiply both the sides by 2, in above expression
\(2x=3y-1\)
add both the sides by 1, in above expression
\(2x+1=3y\)
now, divide above by 3, in above expression
\(\frac{2x+1}{3}=y\)
hence \(f^{-1}(x)=\frac{2x+1}{3}\)
To find \(f^{-1}(4)\), we put x=4 in \(f^{-1}(x)=\frac{2x+1}{3}\)
\(f^{-1}(4)=\frac{2(4)+1}{3}\)
\(f^{-1}(4)=\frac{8+1}{3}\)
\(f^{-1}(4)=\frac{9}{3}\)
\(f^{-1}(4)=3\)
therefore,\(f^{-1}(4)=3\)
