3 years ago

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Mathematics

1 answer:

andrey2020 [161]3 years ago

3 0

Answer:

One possible solution is 5 + i√3.

(there are 2 solutions 5 + i√3 and 5 - i√3).

Step-by-step explanation:

(x - 5)^2 + 5 = 2

(x - 5)^2 = -3

Take square roots of both sides:

x - 5 = √-3

x - 5 = i√3

x = 5 ± i√3.

The solutions are both complex numbers.

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If F(x)=4x-1 and g(x)=x^2+7, what is g(f(x))

VashaNatasha [74]

Answer

$g(f(x)) = = 16 {x}^{2} - 8x + 8$

step by step Explanation

The functions given are

$f (x)= 4x- 1$

$g(x)= {x}^{2} + 7$

We want to find:

$g(f (x))= g( 4x- 1)$

This implies that

$g(f (x))= ( (4x- 1)^{2} + 7)$

Let us now simplify

$( {a - b)}^{2} = {a}^{2} -2ab + {b}^{2}$

This implies that

$( (4x- 1)^{2} + 7) =( {(4x)}^{2} - 2(4x) \times 1 + 1$

Combine the terms to get,

$= 16 {x}^{2} - 8x + 1 + 7$

$= 16 {x}^{2} - 8x + 8$