Questions: Given the function (f(x)=7x-8), calculate the following values: (f(0)=56) (f(2)=42) (f(-2)=70) (f(x+1)=square) (f(x^2+2)=square)

Given the function (f(x)=7x-8), calculate the following values: (f(0)=56) (f(2)=42) (f(-2)=70) (f(x+1)=square) (f(x^2+2)=square)
Transcript text: Given the function $f(x)=7|x-8|$, calculate the following values: \[ \begin{array}{l} f(0)=56 \\ f(2)=42 \\ f(-2)=70 \\ f(x+1)=\square \\ f\left(x^{2}+2\right)=\square \end{array} \]
failed

Solution

failed
failed

Solution Steps

To solve the given problem, we need to evaluate the function \( f(x) = 7|x-8| \) for different values of \( x \). For each part, substitute the given expression into the function and compute the result using the absolute value operation.

Step 1: Evaluate \( f(x+1) \)

The function given is \( f(x) = 7|x-8| \). We need to find \( f(x+1) \).

Substitute \( x+1 \) into the function:

\[ f(x+1) = 7|x+1-8| \]

Simplify the expression inside the absolute value:

\[ x+1-8 = x-7 \]

Thus, the function becomes:

\[ f(x+1) = 7|x-7| \]

Step 2: Evaluate \( f(x^2+2) \)

Next, we need to find \( f(x^2+2) \).

Substitute \( x^2+2 \) into the function:

\[ f(x^2+2) = 7|x^2+2-8| \]

Simplify the expression inside the absolute value:

\[ x^2+2-8 = x^2-6 \]

Thus, the function becomes:

\[ f(x^2+2) = 7|x^2-6| \]

Final Answer

The evaluated expressions are:

\[ \boxed{f(x+1) = 7|x-7|} \]

\[ \boxed{f(x^2+2) = 7|x^2-6|} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. lim as x approaches infinity of sqrt(x) * e^(-x / 2)
failedAnswered
a. Find the least squares line for the data. ŷ = 6.1879 + (-0.0019) x (Round to four decimal places as needed.) b. Interpret β̂₀ and β̂₁ in the words of the problem. Interpret β̂₀ in the words of the problem. A. The regression coefficient β̂₀ is the estimated increase (or decrease) in amount of pectin (in ppm) for each 1-unit increase in sweetness index. B. The regression coefficient β̂₀ is the estimated amount of pectin (in ppm) for orange juice with a sweetness index of 0. C. The regression coefficient β̂₀ is the estimated sweetness index for orange juice that contains 0 ppm of pectin. D. The regression coefficient β̂₀ does not have a practical interpretation.
failedAnswered
Practice for Class Time left 1:44:45 Provide an appropriate response. Which one of the following is the graph of a function? Select one:
failedAnswered
Let p(t) represent the population of the Las Vegas metropolitan area t years after 1970, as shown in the table and figure. Answer parts (a) through (c). Year 1970 1980 1990 t 0 10 20 p(t) 305,000 528,000 853,000 Year 2000 2010 2020 t 30 40 50 p(t) 1,563,000 1,951,000 2,223,000 Source: U.S. Bureau of Census a. Compute the average rate of growth of the city population from 1980 to 1990. The average rate of growth is people/year. (Simplify your answer. Type an integer or a decimal.)
failedAnswered
As part of a statistics project, Charlie would like to collect data on household size in his city. To do so, he asks each person in his statistics class for the size of their household and reports the results of a simple random sample. However, this is not a simple random sample. Why? Charlie did not use any randomization; he took a convenience sample. Charlie did not use a random number table to randomize the order in which he collected the students responses, so the sample cannot be random. In this investigation of household size, each household represents a case. Charlie incorrectly sampled individuals instead of households. Both (a) and (c) are correct. Answers (a), (b), and (c) are all correct.