Question

What is the value of \[f\left( 1 \right)\] if \[f\left( x \right)+f\left( -2x \right)=-6x-12\]?

Answer 1

Hint: In this problem, we have to find the value of \[f\left( 1 \right)\] if \[f\left( x \right)+f\left( -2x \right)=-6x-12\]. We can see that, we are given the value of x, here we have to, just substitute the given 1 in \[x\], in the given equation \[f\left( x \right)+f\left( -2x \right)=-6x-12\] to get the required value. We can then square the first term and add it with the next term to get the final answer.

Complete step-by-step solution:
Here we have to find \[f\left( 1 \right)\].
We know that the given equation is,
\[\Rightarrow f\left( x \right)+f\left( -2x \right)=-6x-12\]
 We can see that from the above given data, we have to find the value of \[f\left( 1 \right)\], so we can substitute the number 1 in the place of x, we get
\[\Rightarrow f\left( 1 \right)+f\left( -2\times 1 \right)=-6\left( 1 \right)-12\]
We can now simplify the above step by adding the terms in the right-hand sides and bringing the terms from the left-hand side to the right-hand side,
\[\Rightarrow f\left( 1 \right)=-f\left( -2\times 1 \right)-6\left( 1 \right)-12\]
We can now simplify the above step by adding the terms in the right-hand side, we get
\[\Rightarrow f\left( 1 \right)=-f\left( -2 \right)-18\]
Therefore, the value of \[f\left( 1 \right)=-f\left( -2 \right)-18\].

Note: Students make mistakes while substituting the value to the variables in the function. We should concentrate while we add the term as we have two negative signs, so we should add them with a negative sign in the result. We can see that we were not provided the value for \[f\left( -2 \right)\], so we can keep them as it is to write the final answer.