Question

If $f:R \to R,$$g:R \to R,$ and $g(x) = x + 3$ and $fog(x) = {(x + 3)^2}$, then the value of f (-3) is
$
  A) - 9 \\
  B)0 \\
  C)9 \\
  D){\text{NONE OF THESE}} \\
 $

Answer 1

Hint: In this problem first we have to find the f(x) with the help of fog(x) and g(x) and then by substituting the value of ‘-3’ in f(x). The value of f (-3) is calculated.

Complete step-by-step answer:

Given here that
  $f:R \to R,$$g:R \to R$
We know that
 $g(x) = x + 3$ ,
   $fog(x) = {(x + 3)^2}$
$ \Rightarrow f(g(x)) = {(x + 3)^2}$
Therefore by using the $f(g(x))$ term we say that
$ \Rightarrow f(y) = {y^2} - - - - > (1)$
Now by using condition (1) let us consider $f(x) = {x^2}$
So here x=-3
Hence then $f( - 3) = {( - 3)^2} = 9$
Therefore the value of f (-3) =9

NOTE: To solve this problem we need to have knowledge about the function concept and the substitutions in function. We should also know the basic terms of function like fog(x) and others.