Use the functions given by and g(x) = x³ to find (f _º g)^-1.

Question

Quizplus · Accepted Answer

First, we need to evaluate f S1U1B1ºS1U1B0 g.

Using the definition of composition of functions:

(f S1U1B1ºS1U1B0 g)(x) = f(S1U1B1(S1U1B0 x)) = f(S1U1P1(x + 2)) = (x + 2)S1U1P13S1S1P0

Next, we need to apply S1U1P1-1S1S1P0 to the result:

((f S1U1B1ºS1U1B0 g)S1U1P1-1S1S1P0)(x) = (f S1U1B1ºS1U1B0 g)(S1U1P1-1S1S1P0 x)

We have:

S1U1P1-1S1S1P0 x = (x - 1)S1S1P0 = xS1S1U1P1S1S1P0S1S1P0

Therefore:

((f S1U1B1ºS1U1B0 g)S1U1P1-1S1S1P0)(x) = (f S1U1B1ºS1U1B0 g)(xS1S1U1P1S1S1P0S1S1P0)

= ((x + 2)S1U1P13S1S1P0)S1S1U1P1S1S1P0S1S1P0

= (x + 2)S1U1P13S1U1P1S1S1P0

= 11eacce6_2229_2ed5_9f49_f95b88e62577_TB7896_11

Therefore, the answer is C.

Use the Functions Given by and G(x) = X3