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Question: How do you find \(g\left( 3 \right)\) given that \(g\left( x \right)=-2{{x}^{2}}-9\)?...

How do you find g(3)g\left( 3 \right) given that g(x)=−2x2−9g\left( x \right)=-2{{x}^{2}}-9?

Explanation

Solution

We try to explain the function and its value at a particular point. For the given function g(x)=−2x2−9g\left( x \right)=-2{{x}^{2}}-9, we need to find the value of the function at x=3x=3. This means we are finding g(3)g\left( 3 \right) for that particular point.

Complete step-by-step solution:
The given problem is about a given function g(x)=−2x2−9g\left( x \right)=-2{{x}^{2}}-9 and the value of the function at that point of x=3x=3 to find g(3)g\left( 3 \right).
So, in those cases we find the value of the function by putting the point x=3x=3 in the function of g(x)=−2x2−9g\left( x \right)=-2{{x}^{2}}-9.
g(3)=−2×32−9g\left( 3 \right)=-2\times {{3}^{2}}-9.
Now we apply the common binary operations to find the value for g(3)g\left( 3 \right).
We need to find the square value of 3 which gives 32=3×3=9{{3}^{2}}=3\times 3=9.
We then multiply the value of the square with 2 and get 9×2=189\times 2=18.
Now the equation becomes g(3)=−18−9g\left( 3 \right)=-18-9.
We have two variables −18-18 and −9-9. The binary operation between them is addition.
This gives g(3)=−18−9=−27g\left( 3 \right)=-18-9=-27.
Therefore, for the given function g(x)=−2x2−9g\left( x \right)=-2{{x}^{2}}-9, the value of g(3)g\left( 3 \right) is −27-27.

Note: The domain of the function has to consist of the value of x=3x=3. The function can give values for only its domain and the values of the function g(x)=−2x2−9g\left( x \right)=-2{{x}^{2}}-9 gives the range for that particular function. In this case −27-27 is an element of the range whereas 3 was an element of the domain.