Question

if f(x)=2x +5 and g(x)=3x-1 upon 2 where fg^-1(x)=f(x) find the value of x​

Answer 1

Answer:

x = 1/2 (correct me if i'm wrong in calculations but the method is correct.)

Step-by-step explanation:

given f(x) = 2x + 5

         g(x) = 3x - 1

and that $f(g^{-1} (x)) = f(x)$

we need to find the inverse of g(x) first

$y= 3x-1\\\frac{y+1}{3} = x$  here we have just represented the equation in terms of y and not x

now replace both variables y and x with each other to get the inverse function g

thus   $g^{-1} (x) = y = \frac{x+1}{3}$

now consider this equation in the question $f(g^{-1} (x)) = f(x)$

all it means is that if you put $g^{-1} (x)$ in the function f(x) then it equals f(x)

or in math terms,

2($g^{-1} (x)$) + 5 = 2x + 5

2($\frac{x+1}{3}$) + 5 = 2x + 5

solve this and you will get your answer.