Question

Find the preimages of 2 and 3 and image of 4 and 5 in the function
$\frac{2x - 3}{5}$
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Answer 1

Answer:

The preimages of 2 and 3 are 6.5 and 9 respectively and images of 4 and 5 are 1 and $\dfrac{7}{5}$ .

Step-by-step explanation:

The image of a number is obtained by substituting the value for x in the definition of the function. Let the function be,

$f(x)=\dfrac{2x-3}{5}$

To find images of 4 and 5, substitute 4 and 5 for x in the above expression.

So the images are given by,

$f(4)=\dfrac{2\times 4-3}{5}=\dfrac{5}{5}=1\\\\f(5)= \dfrac{2\times 5-3}{5}=\dfrac{7}{5}$

So the image of 4 is 1 and the image of 5 is $\dfrac{8}{5}$ .

To find the preimage, we do as follows:

$\dfrac{2x-3}{5}=2\\\\\implies 2x-3=2\times 5=10\\\\\implies 2x= 10+3=13\\\\\implies x=\dfrac{13}{2}=6.5$

$\dfrac{2x-3}{5}=3\\\\\implies 2x-3=3\times 5=15\\\\\implies 2x= 15+3=18\\\\\implies x=\dfrac{18}{2}=9$

So the preimage of 2 is 6.5 and the preimage of 3 is 9.