Question

How do you find the value of $2f(1) + 3g(4)$ if $f(x) = 3x$ and $g(x) = - 4{x^2}$?

Answer 1

Hint: According to given in the question we have to determine the value of $2f(1) + 3g(4)$ if $f(x) = 3x$ and, $g(x) = - 4{x^2}$. So, first of all we have to determine the value of $f(x) = 3x$ where, we have to substitute 1 in the place of x to determine $f(1)$.
Now, we have to determine the value of $g(x) = - 4{x^2}$ where, we have to substitute 4 in the place of x to determine $g(4)$.
Now, we have to substitute the value of $f(1)$ as we have already obtained in the given expression which is $2f(1) + 3g(4)$.
Now, we have to substitute the value of $g(4)$ as we have already obtained in the given expression which is $2f(1) + 3g(4)$.
Hence, on substituting all the values in the expression we can determine the required solution.

Complete step-by-step answer:
Step 1: First of all we have to determine the value of $f(x) = 3x$ where, we have to substitute 1 in the place of x to determine $f(1)$ as mentioned in the solution hint. Hence,
$
   \Rightarrow f(1) = 3(1) \\
   \Rightarrow f(1) = 3 \\
 $
Step 2: Now, we have to determine the value of $g(x) = - 4{x^2}$ where, we have to substitute 4 in the place of x to determine $g(4)$ as mentioned in the solution hint. Hence,
$
   \Rightarrow g(4) = - 4{(4)^2} \\
   \Rightarrow g(4) = - 4 \times 16 \\
   \Rightarrow g(4) = - 64 \\
 $
Step 3: Now, we have to substitute the value of $f(1)$ as we have already obtained in the given expression which is $2f(1) + 3g(4)$ as mentioned in the solution hint. Hence,
$ \Rightarrow 2(3) + 3g(4)$
Step 4: Now, we have to substitute the value of $g(4)$ as we have already obtained in the given expression which is $2f(1) + 3g(4)$ as mentioned in the solution hint. Hence,
$
   \Rightarrow 2(3) + ( - 64) \\
   \Rightarrow 6 - 64 \\
   \Rightarrow - 58 \\
 $

Hence, on substituting the values $f(1)$ and $g(4)$ we have determined the value of the given expression which is -58.


Note:
To obtain the value of the given expression it is necessary that we have to determine the $f(1)$ and $g(4)$ by substituting the values in the expression $2f(1) + 3g(4)$ which is as given in the question.
On substituting all the values we should remember all the signs of positive and negative while solving the expression obtained.