Given the functions f, left bracket, x, right bracket, equals, 5, x, cubedf(x)=5x
3
and g, left bracket, x, right bracket, equals, 2, to the power xg(x)=2
x
, which of the following statements is true?
Answer
Multiple Choice Answers
f, left bracket, 11, right bracket, equals, g, left bracket, 11, right bracketf(11)=g(11)
f, left bracket, 11, right bracket, is greater than, g, left bracket, 11, right bracketf(11)>g(11)
f, left bracket, 11, right bracket, is less than, g, left bracket, 11, right bracketf(11)<g(11)
The correct statement is:
f(11) = g(11)
To determine if f(11) is equal to, greater than, or less than g(11), we need to calculate the values of f(11) and g(11).
The function f(x) is defined as 5x^3, so we can substitute x with 11 to get f(11) = 5 * 11^3 = 5 * 1331 = 6655.
The function g(x) is defined as 2^x, so we can substitute x with 11 to get g(11) = 2^11 = 2048.
Comparing the values, we can see that f(11) is greater than g(11), so the correct statement is:
f(11) > g(11)
To determine which of the following statements is true: f(11) = g(11), f(11) > g(11), or f(11) < g(11), we need to substitute the value of x = 11 into both functions and compare the results.
We are given the functions:
f(x) = 5x^3
g(x) = 2^x
To find f(11), we substitute 11 for x in the function f(x):
f(11) = 5 * 11^3
= 5 * 1331
= 6655
To find g(11), we substitute 11 for x in the function g(x):
g(11) = 2^11
= 2048
Comparing the values, we can see that f(11) = 6655 is greater than g(11) = 2048. Therefore, the correct statement is:
f(11) > g(11)