If `f (x)=x ^(2) , g (x) =5x -6,` then `g [f (x)]=`

Options

A. `26 x ^(2) -60x + 36`
B. `5x ^(2) + 6`
C. `25 x ^(2) + 60x -36`
D. `5x ^(2) -6`

Answer

To solve the problem where \( f(x) = x^2 \) and \( g(x) = 5x - 6 \), we need to find \( g[f(x)] \).

### Step-by-Step Solution:

1. **Identify the functions**:
- We have \( f(x) = x^2 \).
- We have \( g(x) = 5x - 6 \).

2. **Substitute \( f(x) \) into \( g(x) \)**:
- We need to find \( g[f(x)] \), which means we will substitute \( f(x) \) into \( g(x) \).
- So, we will replace \( x \) in \( g(x) \) with \( f(x) \).

3. **Calculate \( g[f(x)] \)**:
- \( g[f(x)] = g[x^2] \).
- Now, substitute \( x^2 \) into the function \( g(x) \):
\[ g[x^2] = 5(x^2) - 6 \]

4. **Simplify the expression**:
- Now, simplify the expression:
\[ g[x^2] = 5x^2 - 6 \]

5. **Final Result**:
- Therefore, \( g[f(x)] = 5x^2 - 6 \).

### Final Answer:
\[ g[f(x)] = 5x^2 - 6 \]