Given the functions f, left bracket, x, right bracket, equals, 5, x, to the power 5f(x)=5x

Question

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)

Answer 1

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)