Answer:
[tex]f^{-1}(4)=3[/tex]
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,
[tex]\frac{3x-1}{2}[/tex]
so,
[tex]y=f(x)=\frac{3x-1}{2}[/tex]
to find inverse of f(x) , we switch x and y,
[tex]x=\frac{3y-1}{2}[/tex]
multiply both the sides by 2, in above expression
[tex]2x=3y-1[/tex]
add both the sides by 1, in above expression
[tex]2x+1=3y[/tex]
now, divide above by 3, in above expression
[tex]\frac{2x+1}{3}=y[/tex]
hence [tex]f^{-1}(x)=\frac{2x+1}{3}[/tex]
To find [tex]f^{-1}(4)[/tex], we put x=4 in [tex]f^{-1}(x)=\frac{2x+1}{3}[/tex]
[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]
