Question

Given $f\left( x \right) = 4x - 3,g\left( x \right) = \dfrac{1}{x}$ and $h\left( x \right) = {x^2} - x$. How do you find $h\left( {kx} \right)?$

Answer 1

Hint: In this question, we are going to solve and find the value of $h\left( {kx} \right)$ and $x$
First we are going to write the given terms and then substitute $x = kx$ in the expression $h\left( x \right)$, we get a value.
Then simplify the terms by equating it to zero, we can get the value of $x$
Hence we can get the required solution.

Complete step by step solution:
In this question, we are going to find the value of $h\left( {kx} \right)$.
First we are going to write the given equation: $f\left( x \right) = 4x - 3$, $g\left( x \right) = \dfrac{1}{x}$and $h\left( x \right) = {x^2} - x$
Now we are going to substitute $x = kx$ in the given expression $h\left( x \right)$ and then we are going to solve the value,
$ \Rightarrow h\left( x \right) = {x^2} - x$
We can express this as
$ \Rightarrow h\left( {kx} \right) = {\left( {kx} \right)^2} - kx$
Squaring the first term we get,
$ \Rightarrow h\left( {kx} \right) = {k^2}{x^2} - kx$
Thus we find the value of $h\left( {kx} \right)$ is ${k^2}{x^2} - kx$
We can take the like terms outside we get,
$ \Rightarrow h\left( {kx} \right) = kx(kx - 1)$

Therefore the value of $h\left( {kx} \right) = kx(kx - 1)$.

Note: Evaluating functions: To evaluate a function, substitute the input (the given number or expression) for the functions variable (placeholder, X). Replace the X with the number or expression.
A function rule describes how to convert an input value into an output value for a given function.
We need to have skills in evaluating functions:
We need the skill in evaluating a function to know how to replace its variable with a given number or expression.