Question

Could someone explain this to me step by step
genuinely confused

Answer 1

Think of x as the input and f(x) as the output. If you plug in -2 in the function, you substitute x as -2 and solve. The same thing goes for x as 0. If f(x) is 4, treat it like you are trying to solve for x. As shown in the diagram, they substituted f(x) as 4 and solved for x and came to the conclusion that x was also 4.

Answer 2

`\boxed{\begin{array}{clc}x&|\:\:F(x)\\-2&|\:\:16\\0&|\:\:4\\4&|\:\:4\end{array}}`

Explanation:

Given:

`\tt F(x)=x^2-4x+4`

Solution:

When x=-2

`\tt f(-2)=(-2)^2-4*(-2)+4`

=4+8+4

=16

The first one is not 12 as we get 16 while solving the number.

`\hrulefill`

When x=0

`\tt f(0)=(0)^2-4*(0)+4`

=0+0+4

=4

The second one is correct as we get 4 while solving.

`\hrulefill`

When f(x)=4

it means

`\tt x^2-4x+4=4`

Doing middle term Factorization:

`\tt x^2-(2+2)x+4=4\\ \tt x^2-2x-2x+4=4`

taking common from each two terms

`\tt x(x-2)-2(x-2)=4\\\tt (x-2)(x-2)=4\\\tt (x-2)^2=4`

square rooting on both sides

`\tt (x-2)=√(4)`

x-2=2

x=2+2

x=4

The third one is correct as we get 4 while solving.