Question

Show that the function g(x)=x+3/2 is the inverse of f(x) = 2x -3

Answer 1

hint:
you have to check that these subsequent conditions hold:
\[\Large g\left( {f\left( x \right)} \right) = 1,\quad f\left( {g\left( x \right)} \right) = 1\]

Answer 2

What do you mean?

Answer 3

for example, I start with the first condition:
\[\Large g\left( {f\left( x \right)} \right) = \frac{{f\left( x \right) + 3}}{2} = \frac{{\left( {2x - 3} \right) + 3}}{2} = ...?\]

Answer 4

Michele, don't you mean "x" instead of "1" in your statement above?

Answer 5

An alternative approach would be to start with f(x)=2x+3 and find the inverse function. Takes only a moment or two.

Rewrite f(x)=2x+3 as y=2x+3. Interchange "x" and "y". Type in your result here.

Answer 6

yes! you are right! Thanks for your reply! :) @mathmale