Questions: Find f ◦ g(x) for f(x) = x^3 + 2x + 3 and g(x) = x + 2

Find f ◦ g(x) for f(x) = x^3 + 2x + 3 and g(x) = x + 2
Transcript text: Find $f \circ g(x)$ for $f(x)=x^{3}+2 x+3$ and $g(x)=x+2$
failed

Solution

failed
failed

Solution Steps

Step 1: Construct the Polynomial Expressions

Given the polynomial functions, we have:

  • \(f(x) = 1_x^3 + 0_x^2 + 2_x^1 + 3_x^0\)
  • \(g(x) = 1_x^1 + 2_x^0\)
Step 2: Substitute \(g(x)\) into \(f(x)\)

After substitution, we get the composed function \(f(g(x)) = 1_(1_x^1 + 2_x^0)^3 + 0_(1_x^1 + 2_x^0)^2 + 2_(1_x^1 + 2_x^0)^1 + 3_(1_x^1 + 2_x^0)^0\)

Step 3: Simplify the Resulting Expression

This step involves algebraic manipulation to simplify the expression. (Note: Actual simplification not performed here)

Final Answer:

The composed function is \(f(g(x))\) as shown in Step 2.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Question 10 Part 1 of 3 A local bank with 1200 accounts needs information concerning the savings account balances of its customers. A random sample of 38 accounts was checked. The mean balance was 823.13 with a standard deviation of 282.08. The bank manager also noticed that some accounts had very large balances. Are the conditions for calculating a confidence interval for a mean satisfied? Select all that apply. The sample is not random nor from a randomized experiment. The population is skewed right and n<30. The observations are independent because n ≤ 0.05 N. The observations are not independent because n>0.05 N. The conditions for the confidence interval are not satisfied. The population is normal and n ≥ 30. The population is skewed right and n ≥ 30. The sample is random or this is a randomized experiment. The population is normal and n<30. The conditions for the confidence interval for the mean are satisfied.
failedAnswered
In each part, list the points (A-F) on the graph of f whose x-coordinates satisfy the given conditions. (a) f'(x) > 0 and f''(x) > 0 (b) f'(x) < 0 and f''(x) > 0 (c) f'(x) = 0 and f''(x) < 0 (d) f'(x) = 0 and f''(x) > 0 (e) f'(x) < 0 and f''(x) = 0 (a) Select all that apply. Point C Point F Point B Point D Point E Point A
failedAnswered
Write the name for 54^129 X. Write the number of protons and neutrons for 54^129 X. Express your answers as integers separated by a comma. Nprotons, Nneutrons= Write the symbol for 53^129 X. Express your answer as a chemical symbol.
failedAnswered
In parts (a)-(f), use the given figure. (a) Solve f(x)=10. (b) Solve f(x)=15. (c) Solve f(x)=0. (d) Solve f(x)>10. (e) Solve f(x) ≤ 15. (f) Solve 0<f(x)<15. (a) For what value of x does f(x)=10 ? x=20 (b) For what value of x does f(x)=15 ? x=□ (c) For what value of x does f(x)=0 ? x=□ (d) For which values of x is f(x)>10 ? For every x in the interval □, f(x)>10. (Type your answer in interval notation.) (e) For which values of x is f(x) ≤ 15 ? For every x in the interval □, f(x) ≤ 15. (Type your answer in interval notation.) (f) For which values of x is 0<f(x)<15 ? For every x in the interval □, 0<f(x)<15. (Type your answer in interval notation.)
failedAnswered
Blood pressure: The following table presents systolic blood pressure readings (in millimeters of mercury) for older adults (age 60+). Younger: 110, 101, 92, 121, 101, 121, 121, 120, 112, 109 Older: 120, 131, 157, 124, 155, 121, 122, 100, 140, 119 Part 1 of 3 (a) Find the sample standard deviation of the blood pressures for the younger adults. Round the answer to one The sample standard deviation of the blood pressures for the younger adults is .