The mapping `f: R rarrR , g, R rarr R` are defined by f(x) `= 5-x^2` and g(x)=3x -4, then find the value of (fog)(-1)

Options

A. 40
B. `-44`
C. `-40`
D. `-45`

Answer

To find the value of \( (f \circ g)(-1) \), we will follow these steps:

### Step 1: Calculate \( g(-1) \)

The function \( g(x) \) is defined as:
\[ g(x) = 3x - 4 \]

Now, substituting \( x = -1 \):
\[ g(-1) = 3(-1) - 4 = -3 - 4 = -7 \]

### Step 2: Calculate \( f(g(-1)) \)

Now that we have \( g(-1) = -7 \), we need to find \( f(-7) \).

The function \( f(x) \) is defined as:
\[ f(x) = 5 - x^2 \]

Substituting \( x = -7 \):
\[ f(-7) = 5 - (-7)^2 = 5 - 49 = 5 - 49 = -44 \]

### Conclusion

Thus, the value of \( (f \circ g)(-1) \) is:
\[ (f \circ g)(-1) = f(g(-1)) = f(-7) = -44 \]

### Final Answer
\[ (f \circ g)(-1) = -44 \]

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