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

How do you find the value of 2f(1)+3g(4)2f(1) + 3g(4) if f(x)=3xf(x) = 3x and g(x)=−4x2g(x) = - 4{x^2}?

Explanation

Solution

According to given in the question we have to determine the value of 2f(1)+3g(4)2f(1) + 3g(4) if f(x)=3xf(x) = 3x and, g(x)=−4x2g(x) = - 4{x^2}. So, first of all we have to determine the value of f(x)=3xf(x) = 3x where, we have to substitute 1 in the place of x to determine f(1)f(1).
Now, we have to determine the value of g(x)=−4x2g(x) = - 4{x^2} where, we have to substitute 4 in the place of x to determine g(4)g(4).
Now, we have to substitute the value of f(1)f(1) as we have already obtained in the given expression which is 2f(1)+3g(4)2f(1) + 3g(4).
Now, we have to substitute the value of g(4)g(4) as we have already obtained in the given expression which is 2f(1)+3g(4)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)=3xf(x) = 3x where, we have to substitute 1 in the place of x to determine f(1)f(1) as mentioned in the solution hint. Hence,
⇒f(1)=3(1) ⇒f(1)=3  \Rightarrow f(1) = 3(1) \\\ \Rightarrow f(1) = 3 \\\
Step 2: Now, we have to determine the value of g(x)=−4x2g(x) = - 4{x^2} where, we have to substitute 4 in the place of x to determine g(4)g(4) as mentioned in the solution hint. Hence,
⇒g(4)=−4(4)2 ⇒g(4)=−4×16 ⇒g(4)=−64  \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)f(1) as we have already obtained in the given expression which is 2f(1)+3g(4)2f(1) + 3g(4) as mentioned in the solution hint. Hence,
⇒2(3)+3g(4)\Rightarrow 2(3) + 3g(4)
Step 4: Now, we have to substitute the value of g(4)g(4) as we have already obtained in the given expression which is 2f(1)+3g(4)2f(1) + 3g(4) as mentioned in the solution hint. Hence,
⇒2(3)+(−64) ⇒6−64 ⇒−58  \Rightarrow 2(3) + ( - 64) \\\ \Rightarrow 6 - 64 \\\ \Rightarrow - 58 \\\

Hence, on substituting the values f(1)f(1) and g(4)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)f(1) and g(4)g(4) by substituting the values in the expression 2f(1)+3g(4)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.