The graph of g(x)=x^3-x is shown. which is the graph of .5g(x-2)+1?

We have the function, .

It can be seen that various transformations are applied to the function g(x) in order to obtain the new function.

As the new function is i.e.

We get that,

The function g(x) is translated to the right by 2 units, then g(x) ⇒ g(x-2).

Further, g(x-2) is shrinked vertically by , which gives g(x-2) becomes .

Finally, the function is translated 1 unit upwards, then ⇒

Hence, the graph of the new function is given below.

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1