Given the functions f, left bracket, x, right bracket, equals, 2, x, to the power 5f(x)=2x
5
and g, left bracket, x, right bracket, equals, 6, dot, 3, to the power xg(x)=6⋅3
x
, which of the following statements is true?
Answer
Multiple Choice Answers
f, left bracket, 9, right bracket, equals, g, left bracket, 9, right bracketf(9)=g(9)
f, left bracket, 9, right bracket, is less than, g, left bracket, 9, right bracketf(9)<g(9)
f, left bracket, 9, right bracket, is greater than, g, left bracket, 9, right bracketf(9)>g(9)
To find the value of f(9), we substitute 9 into the function f(x) and simplify:
f(9) = 2(9)^5 = 2(59049) = 118098
To find the value of g(9), we substitute 9 into the function g(x) and simplify:
g(9) = 6.3^9 = 6(19683) = 118098
Therefore, f(9) is equal to g(9).
The correct statement is: f(9) = g(9)
To determine whether f(9) is equal to, less than, or greater than g(9), we need to evaluate both functions at x = 9.
Let's start with f(x) = 2x^5:
f(9) = 2(9)^5
f(9) = 2(59049)
f(9) = 118098
Now let's evaluate g(x) = 6.3^x:
g(9) = 6.3^9
g(9) ≈ 86325.635
Comparing the evaluated values:
f(9) = 118098
g(9) ≈ 86325.635
From this comparison, we can see that f(9) is greater than g(9).
Therefore, the correct statement is:
f(9) > g(9)
To determine which statement is true, we need to evaluate both f(9) and g(9) and compare the results.
First, let's evaluate f(9) by substituting x = 9 into the function f(x) = 2x^5:
f(9) = 2 * 9^5
f(9) = 2 * 59,049
f(9) = 118,098
Next, let's evaluate g(9) by substituting x = 9 into the function g(x) = 6.3^x:
g(9) = 6.3^9
g(9) = 380,204.032
Now, let's compare the results. Is f(9) equal to g(9), less than g(9), or greater than g(9)?
f(9) = 118,098
g(9) = 380,204.032
Since 118,098 is less than 380,204.032, we can conclude that f(9) is less than g(9).
Therefore, the correct statement is f(9) < g(9).
Answer: f(9) is less than g(9).