Question

How do you find the function value $f\left( x \right)={{x}^{3}}$ for f( - 3) ?

Answer 1

Hint: When we are given a function f(x) in the term of x and then we want to find the value of f(x) when x is equal to k then we can simply put k in the function in place of x. Then we will get the value of f(k).

Complete step by step answer:
The function f(x) is equal to ${{x}^{3}}$ . We will get the value of f(k) when we put k in function in place of x.
So we will get f(- 3) when we put – 3 in ${{x}^{3}}$
Now we can write ${{\left( -3 \right)}^{3}}$ which is equal to – 27
So the value of f(- 3) is equal to – 27

Note:
We always can find the value of f(k) by putting k in the function , but always keep in mind that k should lie in the domain of f , otherwise the value of f(k) will not exist for example in the function ${{\sin }^{-1}}x$ we can put x equal to 2, we can not find the value of f(2) here because the domain of ${{\sin }^{-1}}x$ is from -1 to 1. Inverse of a function will exist when the function is one-one otherwise we can not find the inverse of a function, for example we can not find the inverse of |x| . The domain of f(x) is equal to range of ${{f}^{-1}}\left( x \right)$ and range of f(x) is equal to domain of ${{f}^{-1}}\left( x \right)$ .