if f(x)= log(2)x and g(x)= 2x squared +14, determine the value of (f o g)(5)
To find the value of (f o g)(5), we need to first find the value of g(5), and then substitute that value into f(x).
Let's start by finding the value of g(5). We can do this by substituting x = 5 into the expression for g(x).
g(x) = 2x² + 14
g(5) = 2(5)² + 14
= 2(25) + 14
= 50 + 14
= 64
Now that we know g(5) = 64, we can substitute this value into f(x) to find the value of f(g(5)).
f(x) = log₂(x)
f(g(5)) = log₂(g(5))
= log₂(64)
To evaluate log₂(64), we need to ask ourselves "What power do we need to raise 2 to, in order to get 64?"
2 to the power of what equals 64?
2⁶ = 64
Therefore, log₂(64) = 6.
So, the value of (f o g)(5) is 6.