Question

re f(x) = 2x-5 and g(x)= Žx + 5
inverses? Explain.

Answer 1

We are being asked the inverse of the function f(x) = 2x - 5. Now by definition of an inverse function, f(g(x)) = x. f(x) = 2x - 5, so the inverse would be in the following format:

$=> \mathrm{f\left(g\left(x\right)\right)\:=\:2g\left(x\right)\:\:-\:5}\:$

$=> \mathrm{2g(x) - 5 = x}\:$

$=> \mathrm{2g(x) = x + 5}\:$

$=> \mathrm{g(x) = x + 5 / 2}\:$

I don't understand the inverse function you gave, 'g(x)= Žx + 5' but if it is in other words 'g(x) = x + 5 / 2' then the two functions you gave are inverses.