W(x) = x2 + 1; Find w(x + 3)

Given the function w:

Since we want to find w(x+3), the input would be x+3.

Substitute x = x+3 in.

Alternate Solution

The answer above works if you want it in vertex form. For this alternate solution, I will convert the function in standard form.

As we know:

Therefore:

Now for function w:

Hence:

7

step-by-step explanation:

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5