Answer:
2
Step-by-step explanation:
Here, the given function is,
f(x) = The quantity of 4x plus 1, divided by 3
\(\implies f(x)=\frac{4x+1}{3}\)
The steps that involve in finding the inverse of f(x) are as follows,
Step 1 : Replace f(x) by y,
\(y=\frac{4x+1}{3}\)
Step 2 : Switch x and y,
\(x=\frac{4y+1}{3}\)
Step 3 : Isolate y in the left side of the equation,
\(3x=4y+1\)
\(-4y=1-3x\)
\(y=\frac{1-3x}{-4}\)
\(y=\frac{3x-1}{4}\)
Step 4 : Replace y by \(f^{-1}(x)\),
\(f^{-1}(x)=\frac{3x-1}{4}\)
For x = 3,
\(f^{-1}(3)=\frac{3\times 3-1}{4}=\frac{9-1}{4}=\frac{8}{4}=2\)
Hence, First option is correct.
