Question

Given f(x) = the quantity of 3x minus 1, divided by 2 , solve for f−1(4)

Answer 1

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,$f^{-1}(4)=3$

Answer 2

f(x)=(3x−1)/2<----Starter 
y = (3x-1)/2
switch x and y
x = (3y-1)/2
2x = 3y-1
2x+1 =3y
y = 2/3*x + 1/3 
f^(-1) (x) = 2/3*x + 1/3 
f^(-1) (4) = 2/3*4 + 1/3 = 8/3 + 1/3 = 9/3 = 3

I hope this helps. ;)