Question

What is the value of the function, $f\left( x \right)=7x$, when $x=0.75$ ?

Answer 1

We have been given a mathematical expression and we need to find the output of our equation for a certain value of input. This can be done in two ways. Firstly, we can plot the given mathematical expression and find its output ‘y’ at an input ‘x’. Secondly, we can put the input ‘x’ in the expression to get the output ‘y’. We will be using the second method to answer our problem.

Complete step by step solution:
The mathematical expression given to us is: $f\left( x \right)=7x$ and we need to find the output of this expression for, $x=0.75$.
Let us rewrite the given mathematical expression as:
$\Rightarrow y=7x$
Let us name the above equation as (1). So, we have:
$\Rightarrow y=7x$ ......... (1)
Now, putting the value of ‘x’, that is equal to 0.75 in the above equation, we get:

& \Rightarrow y{{|}_{x=0.75}}=7\times 0.75 \\\ & \therefore y{{|}_{x=0.75}}=5.25 \\\ \end{aligned}$$ Let us name the above equation as (2). So, we have: $$\Rightarrow y{{|}_{x=0.75}}=5.25$$ ......... (2) Thus, the final value of ‘y’ comes out to be 5.25. Now, replacing ‘y’ with $f\left( x \right)$ in equation number (2), we get our final result as: $$\Rightarrow {{\left[ f\left( x \right) \right]}_{x=0.75}}=5.25$$ **Hence, the value of the function, $f\left( x \right)=7x$, when $x=0.75$comes out to be 5.25.** **Note:** We solved our equation using the second method because in this case it was easier and faster to perform a calculation rather than draw a graph and find its value at a certain point. But, there might be some case when the graphical approach would be an easier approach. So, one needs to practice enough to be able to tell what approach to use before starting the problem.