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Mathematics

OpenStudy (grant330sims):

If f(x) = 5x â€“ 3, then what is f*â€“1(x) ?

OpenStudy (jamesj):

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

OpenStudy (jamesj):

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 ...

OpenStudy (jamesj):

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

OpenStudy (jamesj):

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

OpenStudy (anonymous):

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

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