Question

Closed.

Answer 1

Given the equation \[f(x) = \left(\begin{matrix} 5x-3\\ 4\end{matrix}\right)\] which of the below expressions is correct?
a. \[f ^{-1}(x) = \frac{ 3-5x }{ 4 }\]
b.\[f ^{-1}(x) = \frac{4x+3 }{ 5 }\]
c.\[f ^{-1}(x) = \frac{4x-3 }{ 5 }\]
d.\[f ^{-1}(x) = \frac{-5x-3 }{ 4 }\]

Answer 2

@KeithAfasCalcLover

Answer 3

In general to find the inverse of \(f(x)\), you do the following steps:
1.Change \(f(x)\) to \(y\)
2.Exchange \(y\) with \(x\) everywhere in the equation
3. If possible, solve for \(y\)
4. Only if the result is a function swap \(y\) for \(f^{-1}(x)\)
Makes sense so far?

Answer 4

Yup!

Answer 5

So then let's try that; we have:
\[\eqalign{
&f(x)=\frac{5x-3}{4} \\
&y=\frac{5x-3}{4} \\
&x=\frac{5y-3}{4} \\
&4x=5y-3 \\
&4x+3=5y \\
&y=\frac{4x+3}{5} \\
}\]
Since that's still a function, we can revert it back:
\[f^{-1}(x)=\frac{4x+3}{5}\]
So therefore B

Answer 6

Oh! I see! That makes sense. :)

Answer 7

Anytime Captain :D