Question:
Let \(f(x) = x^2\), g(x) = tan x and h(x) = log x. For \(x = \dfrac{\sqrt{\pi}}{2}\), what is the value of [ho(gof)](x)?
मान लीजिए \(f(x) = x^2\), \(g(x) = \tan x\) और \(h(x) = \log x\) है। \(x = \dfrac{\sqrt{\pi}}{2}\) के लिए, \([h \circ (g \circ f)](x)\) का मान क्या है?
Options:
- \(\dfrac{\pi}{2}\)
- \(\dfrac{\pi}{4}\)
- 0
- 1
- \(\dfrac{\pi}{2}\)
- \(\dfrac{\pi}{4}\)
- 0
- 1
Correct Answer: c)
Explanation:
\((g \circ f)(x) = g(f(x)) = \tan(x^2)\).
\([h \circ (g \circ f)](x) = h(\tan(x^2)) = \log(\tan(x^2))\).
For \(x = \dfrac{\sqrt{\pi}}{2}\), \(x^2 = \dfrac{\pi}{4}\).
\([h \circ (g \circ f)]\left(\dfrac{\sqrt{\pi}}{2}\right) = \log(\tan(\pi/4)) = \log(1) = 0\).
\((g \circ f)(x) = g(f(x)) = \tan(x^2)\)।
\([h \circ (g \circ f)](x) = h(\tan(x^2)) = \log(\tan(x^2))\)।
\(x = \dfrac{\sqrt{\pi}}{2}\) के लिए, \(x^2 = \dfrac{\pi}{4}\) है।
अतः \([h \circ (g \circ f)]\left(\dfrac{\sqrt{\pi}}{2}\right) = \log(\tan(\pi/4)) = \log(1) = 0\)।