function p(t) has

a domain of 1 less than or equal to t less than or equal to 12

range of

-40 < p less than or equal to 160

Find the domain and range for. Enter the exact answers

A) P(1/4t+4)

B) -1/10p(2t)+46

To find the domain and range for the given functions, we need to substitute the given values of t into the functions and determine the resulting values.

A) P(1/4t+4)

To find the domain, we need to determine the allowed values for t. The given domain for the function p(t) is 1 ≤ t ≤ 12. We substitute 1/4t + 4 for t:

1 ≤ (1/4t + 4) ≤ 12

Now, we solve this inequality. First, let's subtract 4 from all parts of the inequality:

1 - 4 ≤ (1/4t + 4) - 4 ≤ 12 - 4

-3 ≤ 1/4t ≤ 8

Next, we multiply all parts of the inequality by 4 to eliminate the fraction:

4(-3) ≤ 4(1/4t) ≤ 4(8)

-12 ≤ (1t) ≤ 32

Therefore, the domain for P(1/4t + 4) is -12 ≤ t ≤ 32. (Exact answer for the domain)

To determine the range, we substitute the values of t into the function and analyze the resulting values.

Since we don't have the specific function p(t), we cannot determine the range accurately without more information. However, based on the given range for p(t), -40 < p ≤ 160, we can conclude that the range for P(1/4t + 4) would be:

-40 < p ≤ 160.

B) -1/10p(2t) + 46

To find the domain, we need to determine the allowed values for t. As mentioned earlier, the domain for the function p(t) is 1 ≤ t ≤ 12. We substitute 2t for t:

1 ≤ 2t ≤ 12

Next, we divide all parts of the inequality by 2 to solve for t:

1/2 ≤ (2t)/2 ≤ 12/2

1/2 ≤ t ≤ 6

Therefore, the domain for -1/10p(2t) + 46 is 1/2 ≤ t ≤ 6. (Exact answer for the domain)

Similarly, to determine the range, we would need specific information about the function p(t). Without that information, we cannot accurately determine the range for -1/10p(2t) + 46.