h(4) is defined as g(f(x)) find h(4) as g(x)= 2 lnx
To solve the problem, we need to calculate ( h(4) ). The function ( h(x) ) is defined as ( g(f(x)) ). Let us break this into steps clearly and solve systematically.
Step 1: Understand the Problem
We are given:
- ( g(x) = 2 \ln(x) )
- ( h(x) = g(f(x)) )
We are tasked to find ( h(4) ). That means we need to determine:
[
h(4) = g(f(4))
]
We must know ( f(x) ) explicitly to proceed further because it is necessary for the computation of ( g(f(4)) ).
Step 2: Missing ( f(x) ) Information
Unfortunately, the problem does not define ( f(x) ). If you’re able to provide the definition or expression for ( f(x) ), I can compute this step easily. Without this information, I will assume a generic ( f(x) ) for illustrative purposes and explain the process.
Let us assume ( f(x) ) as an arbitrary function (e.g., ( f(x) = x^2 )) to demonstrate solving ( h(4) ). Once ( f(x) ) is defined, you can substitute directly into the steps provided!
Step 3: Solve ( h(4) ) (Illustrative Example with ( f(x) = x^2 ))
If ( f(x) = x^2 ), then:
[
f(4) = 4^2 = 16
]
Now substitute ( f(4) = 16 ) into ( g(x) = 2 \ln(x) ):
[
g(f(4)) = g(16) = 2 \ln(16)
]
Since ( \ln(16) ) can be expressed as ( \ln(16) = \ln(2^4) = 4 \ln(2) ), we simplify:
[
g(16) = 2 \ln(16) = 2 \cdot 4 \ln(2) = 8 \ln(2)
]
Thus:
[
h(4) = g(f(4)) = 8 \ln(2)
]
Step 4: Determine Exact Value (if needed)
If desired, you can approximate ( \ln(2) ):
[
\ln(2) \approx 0.693
]
Then:
[
h(4) = 8 \ln(2) \approx 8 \cdot 0.693 = 5.544
]
General Process (Without ( f(x) ))
To summarize the process in general terms:
- Compute ( f(4) ).
- Use the result ( f(4) ) as input into ( g(x) = 2 \ln(x) ).
- Evaluate ( g(f(4)) ) to find ( h(4) ).
If ( f(x) ) is given, substitute it directly and follow the steps above.
Please provide ( f(x) ) so I can give the precise value for ( h(4) ) based on the actual function!
Let me know if you have any clarifications, @username!