Question

If (a,8) and (2,b) are ordered pairs which belong to the mapping f:x3x+4 where x ∈R Find a and b

Answer 1

Given:

Function mapping:

$f:x\rightarrow3x+4$ such that $x \in R$.

i.e. value given as input to the function is $x$ and the output is $3x+4$.

Two ordered pairs (a, 8) and (2, b) belong to the above mapping.

To find:

Values

a = ? and b = ?

Solution:

As per the given function, we can write it as:

$y = f(x) =3x+4$

Now, we know that ordered pairs (p, q) are such that p is the value of x (input) and q is the value of y (output).

The ordered pair (a, 8) means value of x = a and y = 8

Let us put both in the given function and find out value of a:

$8 = f(a) =3\times a +4\\\Rightarrow 8 -4 = 3a\\\Rightarrow a = \dfrac{4}{3} = 1.33$

$\therefore \bold{a=1.33}$

Now, let us consider ordered pair (2, b).

Let us put, x = 2 and y = b in the function:

$b = f(2) =3\times2+4\\\Rightarrow b =6+4\\\Rightarrow \bold {b=10}$

Hence, the answers are: a = 1.33 and b = 10