Which statements, if any, are true about these functions? 1. The function f(g(x)) = x for all real x.
II. The function g(xx)) = x for all real x.
III. Functions fand g are inverse functions.
OA. Tonly
B. ll only
O C.
I, II, and III
OD
None of the statements are true.

C)  I, I and III

In other words, statements I through III are all true.

====================================================

Explanation:

Apply substitution to say that,

We can see that the cube root and cube exponents cancel each other out, and everything simplifies to simply x.

Now compute the other composite function, where g(x) is the outer function this time.

Again, the cubing and cube root cancel each other out.

Since both f(g(x)) = x and g(f(x)) = x are true equations, this means that functions f(x) and g(x) are inverses of each other.

The two functions undo one another.

---------

As a simpler example, consider these two functions:

f(x) = x+5

g(x) = x-5

The f(x) function adds 5 to whatever the input is, and the g(x) goes in the opposite direction to subtract 5 to undo what f(x) did. For this example, you should find that f(g(x)) = x and g(f(x)) = x

Applying the composite of these inverses means that the final output is whatever the original input was. If we start with x = 87, then x+5 = 87+5 = 92, and then 92-5 = 87 which was the original input. Overall, no change has happened.

how am i supposed to answer

step-by-step explanation:

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.