Question

If f: R→R defined by f(x) = x^2 + 1 , find f(-4) and also find the pre-image of −3

Answer 1

Answer:

If f: R→R defined by f(x) = x^2 + 1 , find f(-4) and also find the pre-image of − 3. 1. See answer. Add answer.

Answer 2

Step-by-step explanation:

Given:If f: R→R defined by

$f(x) = {x}^{2} + 1$

To find:find f(-4) and also find the pre-image of −3

Solution:

To find the value of f(-4),just put the value

x=-4

$f( - 4) = ( { - 4})^{2} + 1 \\ \\ f( - 4) = 16 + 1 \\ \\ \bold{f( - 4) = 17}$

To find pre image of -3,find the value of x for which the function attains -3

So,

$- 3 = {x}^{2} + 1 \\ \\ {x}^{2} = - 3 - 1 \\ \\ {x}^{2} = - 4 \\ \\ x = \sqrt{ - 4} \\ \\ x = + - 2i$

It is only possible when,x is imaginary.

But the function is defined for Real Numbers to real numbers,

Thus,

There is no pre image of -3 in the domain of function.

Hope it helps you.

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