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Question: How do you evaluate \(f(-1)\) given the function \(f(t)=\dfrac{1}{2}{{t}^{2}}+4\) ?...

How do you evaluate f(−1)f(-1) given the function f(t)=12t2+4f(t)=\dfrac{1}{2}{{t}^{2}}+4 ?

Explanation

Solution

The given polynomial equation that we have been given in this question is f(t)=12t2+4f(t)=\dfrac{1}{2}{{t}^{2}}+4 , we need to substitute the given value of tt in the given polynomial equation, and then we have to compute the following polynomial equation with the given value of tt and the final value we get is the solution of the above given problem and the solution goes as follows:
f(−1)=12(−1)2+4f(-1)=\dfrac{1}{2}{{(-1)}^{2}}+4
Here the given tt value that is to be substituted in the polynomial equation is −1-1, and the polynomial expression is f(t)=12t2+4f(t)=\dfrac{1}{2}{{t}^{2}}+4

Complete step by step solution:
By substituting −1-1 in the polynomial equation the equation is like:
By evaluating the equation found by substituting the value of tt i.e., −1-1
We come across the following calculation,
(−1)2=1{{(-1)}^{2}}=1
Substituting this value in the polynomial equation we get
f(−1)=12(−1)2+4f(-1)=\dfrac{1}{2}{{(-1)}^{2}}+4
⇒\Rightarrow 12(−1)2+4\dfrac{1}{2}{{(-1)}^{2}}+4
By evaluating further,
⇒\Rightarrow 12×1+4\dfrac{1}{2}\times 1+4
⇒\Rightarrow 12+4\dfrac{1}{2}+4
⇒\Rightarrow 1+82\dfrac{1+8}{2}
⇒\Rightarrow 92\dfrac{9}{2}
⇒\Rightarrow 4.54.5
Hence, from the above solution, we have evaluated the given polynomial equation f(t)=12t2+4f(t)=\dfrac{1}{2}{{t}^{2}}+4 by substituting the given value of tt, that is −1-1 and the solution we have found is 4.54.5.

Note: It is possible that sometimes students may find it hard in evaluating the exponent factor of a negative number as given in the above problem, one should be careful in assigning sign to the resulting value after evaluating the exponent part of the negative number. The student also may find difficulty in evaluating the fractional numbers and addition and subtraction of fraction numbers. The main point in this is to substitute -1 in the equation provided. The point to be remembered here is even if they ask for f(1)f\left( 1 \right) we get the same answer as t is squared and we have to solve the same procedure any number that they provide.