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.