Question

How do you find the zero of \[f(x)=9x+5\] ?

Answer 1

Hint: To find the zero of the given function \[f(x)=9x+5\] assume the given equation as equation (1) and solve the problem. As we know that a zero of a function occurs whenever \[f\left( x \right)=0\] . This means \[f\left( x \right)\] will become zero with the value of x when \[f\left( x \right)\] is equal to 0. So let us assume \[f\left( x \right)=0\] and then find the value of x.

Complete step by step solution:
For the given problem we are given a function to find the zero of it.
To find the zero of the given function. Let us consider the given function as equation (1).
\[f(x)=9x+5............\left( 1 \right)\]
As we know that zero function occurs whenever f(x) is equal to 0.
Therefore we have to find the value when the f(x) is equal to 0.
Let us assume that RHS (Right hand side) of equation (1) is equal to 0.
\[9x+5=0\]
Let us consider the above equation as equation (2).
\[9x+5=0............\left( 2 \right)\]
Now, we have to find the value of x.
Subtracting with 5 on both sides of equation (2), we get
\[\begin{align}
  & \Rightarrow 9x+5-5=-5 \\
 & \Rightarrow 9x=-5 \\
\end{align}\]
Let us consider the above equation as equation (3).
\[9x=-5.............\left( 3 \right)\]
Dividing both sides of equation (3) with 9, we get
\[\begin{align}
  & \Rightarrow \dfrac{9x}{9}=\dfrac{-5}{9} \\
 & \Rightarrow x=\dfrac{-5}{9} \\
\end{align}\]
Let us consider the above equation as equation (4).
\[x=\dfrac{-5}{9}.............(4)\]
Therefore, the zero of the function \[f(x)=9x+5\] is \[\dfrac{-5}{9}\].

Note: We can also solve this problem using graph i.e. we have to plot a graph for the equation and therefore zero of the function will be the point at which line intercepts the X-axis. We should note the point that zero of a given function will get at \[f\left( x \right)=0\] but not at \[f\left( 0 \right)\] . If we do \[f\left( 0 \right)\] then we will get the value of y intercept which is not asked in the question.