Question

How do you find $ f\left( {\dfrac{3}{4}} \right) $ given $ f(x) = - 1 + \dfrac{1}{4}x $ ?

Answer 1

Hint: Here we are given a function in terms of “x” and also we are given that the value of “x” and then simplify the expression for the resultant required value.

Complete step by step solution:
Take the given expression: $ f(x) = - 1 + \dfrac{1}{4}x $
Place $ x = \dfrac{3}{4} $ in the above expression –
 $ f\left( {\dfrac{3}{4}} \right) = - 1 + \dfrac{1}{4}\left( {\dfrac{3}{4}} \right) $
Simplify the above expression, first multiplying the two fractions, numerator is multiplied with numerator and the denominator is multiplied with the denominator of the other fraction.
 $ f\left( {\dfrac{3}{4}} \right) = - 1 + \dfrac{3}{{16}} $
Take LCM (Least common multiple) for the above expression.
 $ f\left( {\dfrac{3}{4}} \right) = - \dfrac{{16}}{{16}} + \dfrac{3}{{16}} $
When denominators are the same, numerators are combined.
 $ f\left( {\dfrac{3}{4}} \right) = \dfrac{{ - 16 + 3}}{{16}} $
When you simplify between one negative term and one positive term, you have to do subtraction and give signs of bigger numbers to the resultant value.
 $ f\left( {\dfrac{3}{4}} \right) = \dfrac{{ - 13}}{{16}} $
This is the required solution.
So, the correct answer is “ $ f\left( {\dfrac{3}{4}} \right) = \dfrac{{ - 13}}{{16}} $ ”.

Note: Always cross check the given expression and then place the value of “x” and be careful about the sign convention. Be careful about the sign while doing simplification and remember the golden rules-
I.Addition of two positive terms gives the positive term
II.Addition of one negative and positive term, you have to do subtraction and give sign of bigger numbers whether positive or negative.
III.Addition of two negative numbers gives a negative number but in actual you have to add both the numbers and give a negative sign to the resultant answer.