If f(x) = ln x and g(x) = ex then find the value of f o g (2/3) ?
If f(x) = ln x and g(x) = ex then find the value of f o g (2/3) ?
Answer: A. 2/3 — Concept: For functions f and g, the composition (f∘g)(x) means substitute g(x) in place of x inside f — that is, (f∘g)(x) = f(g(x)). A key identity used here:…
- A.
2/3
- B.
1/3
- C.
4/3
- D.
None of these
Show answer & explanation
Correct answer: A
Concept: For functions f and g, the composition (f∘g)(x) means substitute g(x) in place of x inside f — that is, (f∘g)(x) = f(g(x)). A key identity used here: the natural logarithm and the exponential function are exact inverses, so ln(ex) = x for every real x.
Evaluate the inner function first: g(2/3) = e2/3.
Substitute this into f: (f∘g)(2/3) = f(e2/3) = ln(e2/3).
Apply the inverse identity ln(ex) = x with x = 2/3: ln(e2/3) = 2/3.
Cross-check: since (f∘g)(x) = ln(ex) = x holds for every x, substituting x = 2/3 directly gives the same result, 2/3 — confirming the step-by-step computation.
Hence, (f∘g)(2/3) = 2/3.