If `f : R to R, g : R to R and h: R to R` is such that `f (x) =x ^(2) , g (x) = tan x and h (x) = log x, ` then the value of `[ho(gof),if x = (sqrtpi)/(2)` will be

Answer

To solve the problem, we need to evaluate the expression \( h \circ g \circ f \) at \( x = \frac{\sqrt{\pi}}{2} \). Let's break it down step by step.

### Step 1: Define the functions
We have the following functions:
- \( f(x) = x^2 \)
- \( g(x) = \tan(x) \)
- \( h(x) = \log(x) \)

### Step 2: Compute \( f\left(\frac{\sqrt{\pi}}{2}\right) \)
We first need to find \( f\left(\frac{\sqrt{\pi}}{2}\right) \):
\[ f\left(\frac{\sqrt{\pi}}{2}\right) = \left(\frac{\sqrt{\pi}}{2}\right)^2 = \frac{\pi}{4} \]

### Step 3: Compute \( g(f(x)) \)
Next, we need to compute \( g(f(x)) \):
\[ g\left(f\left(\frac{\sqrt{\pi}}{2}\right)\right) = g\left(\frac{\pi}{4}\right) = \tan\left(\frac{\pi}{4}\right) \]
Since \( \tan\left(\frac{\pi}{4}\right) = 1 \), we have:
\[ g\left(f\left(\frac{\sqrt{\pi}}{2}\right)\right) = 1 \]

### Step 4: Compute \( h(g(f(x))) \)
Now we compute \( h(g(f(x))) \):
\[ h\left(g\left(f\left(\frac{\sqrt{\pi}}{2}\right)\right)\right) = h(1) = \log(1) \]
Since \( \log(1) = 0 \), we have:
\[ h\left(g\left(f\left(\frac{\sqrt{\pi}}{2}\right)\right)\right) = 0 \]

### Final Answer
Thus, the value of \( h \circ g \circ f \) at \( x = \frac{\sqrt{\pi}}{2} \) is:
\[ \boxed{0} \]