Question

What is the value of x if \[f\left( x \right)=15\]? The actual function of \[x=3x-5\] over \[x+1\]. How to find x?

Answer 1

Hint: For solving this question you should know about the finding the values of functions if the functions solution is also given. We will solve this question by taking the value of \[f\left( x \right)\] equal to the value of the function. And here the function is given as a fractional form.

Complete step by step answer:
According to our question we have to find the value of x, when the value of the function is 1.5 and the actual function is \[x=3x-5\] over \[x+1\].
Since, as we know that the value of any function is equal to the function which can be in anyone form. So, according to our question,
We can write that the function is \[\dfrac{3x-5}{x+1}\].
And the value of this function is 15.
So, we can write it as: \[\dfrac{3x-5}{x+1}=15\].
We have to solve this.
So, for solving this question we will solve our function which is represented here as a fractional form.
Now, the function is \[\dfrac{3x-5}{x+1}=15\].
If we multiply \[\left( x+1 \right)\] both sides then:
\[\begin{align}
  & \Rightarrow 3x-5=15\left( x+1 \right) \\
 & \Rightarrow 3x-5=15x+15 \\
\end{align}\]
If we take all variable terms one side and others in one side L.H.S. and R.H.S. respectively, then:
\[\begin{align}
  & \Rightarrow 3x-15x=15+5 \\
 & \Rightarrow -12x=20 \\
 & \Rightarrow x=\dfrac{20}{-12} \\
 & \Rightarrow x=-{}^{5}/{}_{3} \\
\end{align}\]
So, here the value of x, if \[f\left( x \right)=15\] and the actual function if \[x=3x-5\] over \[x+1\], is the \[-{}^{5}/{}_{3}\].

Note: For calculating the value of x like in these questions you should always use the value of the function for calculating value and if the function is given for more powers then we can get more than one value for the x. But we have to be careful with the power and calculations.