Find g (x) if it is known that g (2t) = 8t-1.

g (x) = 4x - 1

Step-by-step explanation:

Linear function in the format: g (x) = ax + b

g (2t) is a * (2t) + b

g (2t) = 8t - 1 means that:

when x = 2t, g = 8t - 1.

So

Equaling both sides

8t - 1 = a*2t + b

So

b = - 1,

and

2a = 8, a = 8/2, a = 4

So

g (x) = 4x - 1