Question

consider the function f: R to R defined by f(x) = 2x+5, tet a function g:1/2(x - 5)prove that g is an inverse of f​

Answer 1

Answer:

$f : R \rightarrow R$

$f(x)= 2x+5$

Now to prove that g is inverse of f we just need to show that

$f(g(x))=x$

Now,

$f(g(x)) = f(\frac{1}{2} (x-5))$

$f(g(x)) = 2(\frac{1}{2} (x-5))+5 = x$

$\text{hence, } g^{-1} = f$