Question

If fog(x)=((2x-1)/x) and g(x)=5x+2. find f(x)

Answer 1

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Answer:

f(x) = (2x -9)/(x -2)

Explanation:

We can use the fact that g(g^-1(x)) = x.

`(f\circ g)(x) = f(g(x))\\\\(f\circ g)(g^(-1)(x))=f(g(g^(-1)(x)))=f(x)`

So, we need to know the inverse of g(x):

x = g(y)

x = 5y +2

x -2 = 5y

y = (x -2)/5 . . . . inverse of g(x)

Then we have ...

`f(x)=(f\circ g)(g^(-1)(x))=(f\circ g)\left((x-2)/(5)\right)\\\\f(x)=(2\left((x-2)/(5)\right)-1)/(\left((x-2)/(5)\right))=(2x-4-5)/(x-2)\\\\\boxed{f(x)=(2x-9)/(x-2)}`