Question

If f(x) = 5x – 3, then what is f*–1(x) ?

Answer 1

Write the equation
\[ y = f(x) = 5x - 3 \]
Now solve for \( x = g(y) \). The function \( g \) is the inverse function \( f^{-1} \).

Answer 2

Hence in this case,
\[ y = 5x - 3 \]
\[ 5x = y + 3 \]
\[ x = g(y) = \frac{1}{5}(y+3) \]
In other words, the inverse function is ...

Answer 3

\[ f^{-1}(x) = \frac{1}{5}(x+3) \]

Answer 4

You should verify this now by showing that
\[ f(f^{-1}(x)) = x \] and
\[ f^{-1}(f(x)) = x \]

Answer 5

\[f^{-1}(5x-3)=x\] Let \[y=5x-3\]
then find x in terms of y and sub back to the 1st equation.