Find the inverse of the function. Is the inverse a function? f(x) = (x − 2)2

Step-by-step explanation:

Given function is,

f(x) = (x - 2)²

Step - 1

Rewrite the function in the form of a equation.

y = (x - 2)²

Step - 2

Interchange the variables 'x' and 'y',

x = (y - 2)²

Step - 3

Solve the equation for y,

x = (y - 2)²

y - 2 = √x

y = 2 + √x

Step - 4

Rewrite the equation in the form of a function,

a

explanation:

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct