Question

How do you evaluate the function with the given values of x: $h(x)=23x-1$; $x=\dfrac{1}{3}$ ; $x=-1$ ?

Answer 1

Hint: In this question, we have to find the value of a function given in the problem. Thus, we will use the substitution method and the basic mathematical rules to get the solution. First, we will substitute the value of x as $\dfrac{1}{3}$ in the equation h(x). Then, we will take the least common multiple of the denominator and make the necessary calculations, to get the value of the function. Similarly, we will substitute the value of -1 in the function and make the necessary calculations, to get the solution.

Complete step by step solution:
According to the question, we have to find the value of the function.
Thus, we will use the substitution method and the basic mathematical rules to get the solution.
The equation given to us is $h(x)=23x-1$ --------- (1)
(i) $x=\dfrac{1}{3}$
First, we will substitute the value $\dfrac{1}{3}$ in place of x in the equation (1), we get
$\Rightarrow h\left( \dfrac{1}{3} \right)=23\left( \dfrac{1}{3} \right)-1$
On further simplification, we get
$\Rightarrow h\left( \dfrac{1}{3} \right)=\dfrac{23}{3}-1$
Now, we will take the least common multiple on the right-hand side in the above equation, we get
$\Rightarrow h\left( \dfrac{1}{3} \right)=\dfrac{23-3}{3}$
On further solving, we get
$\Rightarrow h\left( \dfrac{1}{3} \right)=\dfrac{20}{3}$ which is the solution.
(ii) $x=-1$
Now, we will substitute the value -1 in place of x in the equation (1), we get
$\Rightarrow h\left( -1 \right)=23\left( -1 \right)-1$
Now, we will open the brackets on the right-hand side in the above equation, we get
$\Rightarrow h\left( -1 \right)=-23-1$
On further solving, we get
$\Rightarrow h\left( -1 \right)=-24$ which is the solution.
Therefore, for the function $h(x)=23x-1$ ; when $x=\dfrac{1}{3}$ , the value of function is equal to $h\left( \dfrac{1}{3} \right)=\dfrac{20}{3}$ and when $x=-1$ , the value of function is equal to $h\left( -1 \right)=-24$ .

Note:
While solving this problem, do mention every step properly to avoid mathematical error and confusion. Do not forget to write the value of x in the function to get an accurate answer.