Given the functions f, left bracket, x, right bracket, equals, 5, x, to the power 5f(x)=5x
5
and g, left bracket, x, right bracket, equals, 6, to the power xg(x)=6
x
, which of the following statements is true?
Answer
Multiple Choice Answers
f, left bracket, 7, right bracket, equals, g, left bracket, 7, right bracketf(7)=g(7)
f, left bracket, 7, right bracket, is less than, g, left bracket, 7, right bracketf(7)<g(7)
f, left bracket, 7, right bracket, is greater than, g, left bracket, 7, right bracketf(7)>g(7)
To compare the values of f(7) and g(7), we need to substitute x=7 into the equations for f(x) and g(x).
For f(x)=5x^5, f(7) would be equal to 5(7)^5 = 5(16807) = 84035.
For g(x)=6^x, g(7) would be equal to 6^7 = 279936.
Since f(7) is less than g(7), the correct statement is:
f(7) < g(7)
To find out if f(7) is equal to, less than, or greater than g(7), we need to evaluate both functions at x = 7.
Let's evaluate f(x) at x = 7:
f(7) = 5(7)^5 = 5 * 7^5 = 5 * 16807 = 84035.
Next, let's evaluate g(x) at x = 7:
g(7) = 6^7 = 279936.
Comparing the values, we have:
f(7) = 84035
g(7) = 279936
Since 84035 is less than 279936, the correct statement is:
f(7) is less than g(7) => f(7) < g(7).
To determine which statement is true, we need to evaluate the functions f(x) and g(x) at x = 7 and compare the results.
First, let's evaluate f(7):
f(x) = 5x^5
f(7) = 5(7^5)
f(7) = 5(16807)
f(7) = 84035
Now, let's evaluate g(7):
g(x) = 6^x
g(7) = 6^7
g(7) = 279936
Comparing the values, we can see that f(7) = 84035 is greater than g(7) = 279936. Therefore, the correct statement is:
f(7) is greater than g(7) -> f(7) > g(7)