if any two function f and g : R→ R

f(x) = 3x+4

and gof(x) = 2x-1

then find g(x) ?????

f(x) = 3x+4

And gof(x) = 2x-1
gof(x) means g(f(x)) , it means in the function of g(x) , put the value obtained from f(x).

Let g(x) = ax +b
So g(f(x) = a(f(x)) +b = a(3x+4) +b = 3ax + 4a + b
This is equal to 2x -1
So equating the coefficient of x and constant, we have ,
4a + b = -1
And 3a = 2
So a = 2/3 , and b = -11/3

Hence g(x) = 2/3x - 11/3 (ans)


 

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g(x) should also be a linear function. Let g(x) = ax+b

Then gof(x) = 3ax + 4a +b = 2x - 1

Hence a=2/3 and b=-11/3

Hence g(x) = 2x/3 - 11/3.

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