Question

Given the functions
f(x)=x+5/3 and g(x)=1/f^-1(x)+1, find the value of g(3).

The first step would first be to find the inverse of x+1, the denominator of the fraction. I think the inverse would be 1-x. And now we have 1/1-x so we can just plu in 3. Right?

Answer 1

I have a feeling you meant f(x) = (x+5)/3
or is it the way you typed it ?

confirm please

Answer 2

Yes it is (x+5)/3 thank you for correcting me.

Answer 3

Given the functions
f(x)=(x+5)/3 and g(x)=1/f^-1(x)+1, find the value of g(3).

The first step would first be to find the inverse of x+1, the denominator of the fraction. I think the inverse would be 1-x. And now we have 1/1-x so we can just plu in 3. Right?

Answer 4

f(x) = (x+5)/3
f^-1(x) = 3x-5
g(x) = 1/(f^-1(x)+1) = 1/(3x-4)
g(3) = 1/5

Of course, you might also have meant just what you typed, in which case

g(x) = 1/f^-1(x) + 1 = 1/(3x-5) + 1 = (3x-4)/(3x-5)
and so g(3) would be 5/4