Question

(fog)(x)=7x-1÷3 and f(x)= 3x+5 find g(x) , where g(x) is linear .

Answer 1

Answer:

Let g(x) = ax + b, where a, b are real numbers.

f(g(x)) = 3 (ax + b) + 5 = 3ax + 3b + 5

= (7x - 1)/3 = 7/3 x - 1/3

By correspondence, 3a = 7/3, so a = 7/9

3b + 5 = -1/3

3b = - 16/3

So b = -16/9

Thus g(x) = 7/9 x - 16/9