F(x)= x+1/2 and g(x)= 2x+1?

Question

f(x)= x+1/2 and g(x)= 2x+1

solve the equation

g^-1(x)=1

Answer 1

I can see that the question is asking for the inverse function of g(x), but I don't know why they put f(x)....anyways here is my answer:

to find the inverse of g(x)=2x+1:

we write it: y=2x+1

replace the x and y:  x=2y+1

solve for y:  -2y= -x+1

2y=x-1

y= (1/2)x - 1/2

which means that: g^-1(x)= (1/2)x - 1/2

given in the question that g^-1(x)=1:  (1/2)x - 1/2=1

solve to find the value of x: (1/2)x = 3/2

multiply by 2: x= 3

hope this helps:)