If `f(t) =sqrt(t), g(t)=t//4 and h(t)=4t-8`, then the formula for `g(f(h(t)))` will be

Options

A. `(sqrt(t-2))/(4)`
B. `2sqrt(t)-8`
C. `(sqrt((4t-8)))/(4)`
D. `(sqrt((t-8)))/(4)`

Answer

To find the formula for \( g(f(h(t))) \), we will follow these steps:

1. **Identify the Functions**:
- \( f(t) = \sqrt{t} \)
- \( g(t) = \frac{t}{4} \)
- \( h(t) = 4t - 8 \)

2. **Calculate \( h(t) \)**:
- We already have \( h(t) = 4t - 8 \).

3. **Calculate \( f(h(t)) \)**:
- Substitute \( h(t) \) into \( f(t) \):
\[ f(h(t)) = f(4t - 8) = \sqrt{4t - 8} \]

4. **Calculate \( g(f(h(t))) \)**:
- Now substitute \( f(h(t)) \) into \( g(t) \):
\[ g(f(h(t))) = g(\sqrt{4t - 8}) = \frac{\sqrt{4t - 8}}{4} \]

5. **Final Result**:
- Therefore, the formula for \( g(f(h(t))) \) is:
\[ g(f(h(t))) = \frac{\sqrt{4t - 8}}{4} \]