Question

Find the value of $15{x^7} + {x^6} + x$ if $x = 7.$

Answer 1

Hint: Here, a function is given, to find the value of function at x = 7 put x = 7 in function i.e. replace x by 7 in given function to get the result.

Complete step by step answer:
Let given function, $f(x) = 15{x^7} + {x^6} + x$
Here, f(x) is a polynomial function.
Therefore, the given function is defined for all real values, so we can find its value at x = 7.
[Since a polynomial function is defined for all real values]
To find the value of function at x = 7, put x = 7 in f(x).
$f(7) = 15 \times {\left( 7 \right)^7} + {\left( 7 \right)^6} + 7$
By simplifying, we get
$
  f(7) = 15 \times 823543 + 117649 + 7 \\
   \Rightarrow f(7) = 12353145 + 117656 = 12470801 \\
 $
Therefore, the value of the given function at x = 7 is 12470801.


Note:
 In these types of questions, you can simply get the value of the function at any value of its domain. In the above question, the given function is simple and we can’t simplify it further, so we have to just put the value of x at which value of the function is asked. But in case if the given function is not simple and linear, first simplify the given function and then put the value at which the value of the function is asked.
Some important points:
Function: It is a relation between the dependent and independent variables and is denoted by y or f(x).
Value of a function: The value of a function y = f(x) at x = a is denoted by putting “a” in place of x in f(x).
Different types of functions:
Constant function, Identity function, Polynomial function or Algebraic function, Rational function, Irrational function, Modulus function, Transcendental function, etc.